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Нелинейная динамика

Нелинейная динамика — междисциплинарная наука, в которой изучаются свойства нелинейных динамических систем. Нелинейная динамика использует для описания систем нелинейные модели, обычно описываемые дифференциальными уравнениями и дискретными отображениями.
Нелинейная динамика включает в себя теорию устойчивости, теорию динамического хаоса, теорию интегрируемых систем.

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World Scientific Publishing, Singapore, 1993, 158 Pages This is a series of lecture notes on nonlinear dynamics for physicists. The level is that of an advanced undergraduate or beginning graduate student. The main aim of these lectures is to present a balance of qualitative and quantitative material. The book also aims to address three main questions about nonlinear dynamics:...
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Springer International Publishing AG, 2018. — 238 p. — ISBN 3319781928. This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular,...
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Springer International Publishing AG, 2018. — 224 p. — ISBN 3319781928. This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular,...
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Cambridge University Press, 2011. — 362 p. — ISBN 978-1-10766-410-4. The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class...
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Addison-Wesley, 1992. — 642 p. — (Studies in Nonlinearity). — ISBN 0-20156-717-2. The book shows a new way to learn a new mathematics - it is a visual tour that's accessible to a wide range of academic levels. During the Renaissance, algebra was resumed from Near Eastern sources, and geometry from the Greek. Scholalrs of the time became familiar with classical mathematics....
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New York: Springer, 2014. - 297 p. This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as...
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Springer, 2017. — 175 p. — (Nonlinear Physical Science). — ISBN 978-981-10-3179-3. This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to...
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New York: Springer, 1996. - 612 pp. На англ. яз. Chaos: An Introduction to Dynamical Systems is a new textbook aimed at introducing the world of nonlinear dynamics and chaos to students in mathematics and the sciences. The authors' goal is to explain the basic concepts in a way that reflects the wide range of influences present during the development of nonlinear dynamics, from...
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New York: Springer, 2018. — 252 p. This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly...
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New York: Springer, 2010. — 254 p. The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular...
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Boston: Kluwer, 2000. — 215 p. Stochastic Resonance: Theory and Applications deals with the theory of noise-added systems and in particular with Stochastic Resonance, a quite novel theory that was introduced in the 1980s to provide better understanding of some natural phenomena (e.g. ice age recurrence). Following the very first works, a number of different applications to both...
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Springer International Publishing AG, 2017. — 297 p. — (Contributions to Statistics) — ISBN 978-3-319-55845-5. This volume collects latest methodological and applied contributions on functional, high-dimensional and other complex data, related statistical models and tools as well as on operator-based statistics. It contains selected and refereed contributions presented at the...
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Springer, 2007. — 461 p. This book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. It contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results in a field to which the authors have made important contributions themselves. Despite the unified presentation of the...
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Springer, 2014. - 300 p. - This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of...
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New York: John Wiley & Sons, 2003. — 254 p. The time operator is a powerful method for the study of unstable dynamics and chaos theory. This synthesis of classical and modern material provides a highly applied approach to the development of both spectral analysis and prediction for chaotic complex systems for which the time operator is described by a semigroup of operators.
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Taylor & Francis, 2002. - 580 pages. The field of nonlinear dynamics and low-dimensional chaos has developed rapidly over the past twenty years. The principal advances have been in theoretical aspects but more recent applications in a wide variety of the sciences have been made. Nonlinear Dynamics and Chaos in Semiconductors is the first book to concentrate on specific physical...
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Springer, 2018. — 340 p. The present book is the second volume and it is dedicated to nonlinear physics. This is a very large area of research including subjects as regulation and morphogenesis of living systems, nonlinear hydrodynamic waves, gravitational waves, ocean circulation, drug resistance, black holes, brain tumors, antifreeze proteins, dark matter waves, neural...
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Springer, 2011. — 327 pages. The ECCOMAS Thematic Conference Multibody Dynamics 2009 was held in Warsaw, representing the fourth edition of a series which began in Lisbon (2003), and was then continued in Madrid (2005) and Milan (2007), held under the auspices of the European Community on Computational Methods in Applied Sciences (ECCOMAS). The conference provided a forum for...
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B.: Springer, 2010. - 591p. The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are...
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Springer International Publishing AG, 2017. — 336 p. — (Nonlinear Systems and Complexity 20) — ISBN: 9783319536729. This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I....
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Cambridge University Press, 1990. — 79 p. — ISBN 0521303621, 0521316502. Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior." The first portion of the book is based on lectures given at the University of London and covers the background to...
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Chapman & Hall, 1992. - 330 pages. In recent years there has been unprecedented popular interest in the chaotic behavior of discrete dynamical systems. The ease with which a modest microcomputer can produce graphics of extraordinary complexity has fired the interest of mathematical-minded people from pupils in schools to postgraduate students. At undergraduate level, there is a...
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Chapman & Hall, 1992. - 330 pages. This text discusses the qualitative properties of dynamical systems including both differential equations and maps, The approach taken relies heavily on examples (supported by extensive exercises, hints to solutions and diagrams to develop the material including a treatment of chaotic behaviour. The unprecedented popular interest shown in...
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Journal. Open Academic Press. 2013 — 496 p. Introduction - Norma B. Crosby Theoretical Models of SOC Systems - Markus J. Aschwanden SOC and Fractal Geometry - R. T. James McAteer Percolation Models of Self-Organized Critical Phenomena - Alexander V. Milovanov Criticality and Self-Organization in Branching Processes: Application to Natural Hazards - Álvaro Corral,...
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Berlin/Boston, Germany: Walter de Gruyter GmbH, 2016. — 149 p. — ISBN 3110460866. This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit...
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Springer, 2018. — 411 p. — (Springer Proceedings in Mathematics & Statistics 248). — ISBN 978-3-319-96597-0. This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life...
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Amsterdam: Springer, 2008. — 342 p. This volume contains the invited papers presented at the 9th International Conference Dynamical Systems Theory and Applications held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics...
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Singapore: World Scientific, 2007. - 320p. This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in...
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Springer, 1998. — 316 p. How well is Nature simulated by the varied asymptotic models that imaginative scientists have invented? This book deals with asymptotic methods in nonlinear dynamics. For the first time a detailed and systematic treatment of new asymptotic methods in combination with the Pade approximant method is presented. Most of the basic results included in this...
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InTech, 2012. - 355 p. - This book focuses on introducing both theoretical and application oriented approaches in science and engineering. It is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos. Contents Applications of 2D...
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Springer, 2004. — 341 p. — ISBN 978-3-642-05810-3. This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different...
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Academic Press, 2018. — 718 p. — (Advances in Nonlinear Dynamics and Chaos). — ISBN 978-0-12-816152-4. This book consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms,...
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Elsevier, 2018. — 680 p. — ISBN 978-0-12-813592-1. This book illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order...
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Cambridge University Press, 1996, 255 p. Books that take you from undergraduate physics to a nontrivial understanding of nonlinear dynamics, chaos and fractals are rare. Chaotic Dynamics does the job ellegantly. The familiar pendulum is used to illustrate the basic techniques and concepts in nonlinear dynamics. The reader is gently introduced to phase diagrams, Poincare sections,...
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N.-Y.: Springer, 2008. - 284p. This book is an introduction to the multidisciplinary field of anomalous diffusion in complex systems, with emphasis on the scaling approach as opposed to techniques based on the quantitative analysis of underlying transport equations. Typical examples of such systems are turbulent plasmas, convective rolls, zonal flow systems and stochastic...
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3rd Edition. — NY, USA: W. H. Freeman and Company, 2014. — 756 p. — ISBN 3906980472. Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and...
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Springer New York Dordrecht Heidelberg London, 2012. X, 310 p. — ISBN 978-1-4614-0456-9, e-ISBN 978-1-4614-0457-6 Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s...
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John Wiley & Sons Ltd, West Sussex, UK, 2016. — 306 p. — ISBN 1119015642. Arun K. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics. This book describes how to build mathermatical models of multibody systems with elastic components. Examples of such systems include the human body itself, construction cranes, cares with trailers,...
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Springer, 1980. — 308 p. Proceedings, Universite de Paris XIII, Villetaneuse, France, October 2-4, 1978.
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Contents. Acknowledgements. ntroduction. The chaos game. Attractors of iterated function systems. Another chaos game. Codes, metrics and topologies. ntroduction. Points and spaces. Functions, mappings and transformations. Addresses and code spaces. Metric spaces. Metrics on code space. Cauchy sequences, limits and continuity. Topological spaces. mportant basic...
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Springer Science+Business Media, New York, 2013. — 296 p. — ISBN: 0817683992 This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals,...
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Birkhauser, 2010. - 440 p. - This book - an outgrowth of an international conference held in honor of Jacques Peyrière - provides readers with an overview of recent developments in the mathematical fields related to fractals. Included are original research contributions as well as surveys written by experts in their respective fields. The chapters are thematically organized into...
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Springer International Publishing AG, 2017. — 320 p. — (Trends in Mathematics) — ISBN 978-3-319-57803-3. The fractals in mathematics are old. The first examples from the end of the nineteenth century are probably Cantor’s ternary set and the graphs of continuous nowhere differentiable functions of Riemann, Weierstrass and others. The main tools for studying fractals are various...
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Springer, 2012. — 213 p. — ISBN: 1447148347 The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction. Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a...
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Springer, 1990. — 229 p. Proceedings of the 6th Interdisciplinary Workshop on Nonlinear Coherent Structures in Physics, Mechanics, and Biological Systems Held at Montpellier, France, June 21–23, 1989. This book is devoted to the applications of the mathematical theory of solitons to physics, statistical mechanics, and molecular biology. It contains contributions on the signature...
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New York: Wiley-ISTE, 2013. - 506 p. This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities. The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal...
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Oxford: Oxford University Press, 1991. — 385 p. This volume originated as a series of lectures given at the workshop Hyperbolic Geometry and Ergodic Theory' held at the International Centre for Theoretical Physics in Trieste, 17-28 April, 1989. Hyperbolic geometry and surfaces of negative curvature were crucial to the early development of ergodic theory, so the two subjects have a...
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Springer, 2017. — 284 p. — ISBN 978-3-319-50763-7. This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary,...
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Springer, 2015. — 338 p. Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a...
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Springer, 2007, 304 pages This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group and self-consistent mode coupling. Dynamic critical phenomena near a second order...
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Springer International Publishing AG, 2018. — 120 p. — (SpringerBriefs in Applied Sciences and Technology). – ISBN 3319709925. This book describes systematic design techniques for chaotic and hyperchaotic systems, the transition from one to the other, and their implementation in electronic circuits. It also discusses the collective phenomena manifested by these systems when...
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Springer-Verlag Berlin Heidelberg 1998. — (Theoretical and Mathematical Physics). — 350 pp. — ISBN: 978-3-642-63780-3 (Print) 978-3-642-58893-8 (Online). This is a modern approach to Hamiltonian systems where multi-Hamiltonian systems are presented in book form for the first time. These systems allow a unified treatment of finite, lattice and field systems. Having more than one...
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Cambridge University Press, 2018. — 266 p. — ISBN 978-1-107-05626-8. A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems,...
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New York: Springer, 2016. - 201p. These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan...
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Boston: Birkhäuser, 2012. — 369 p. The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of...
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Springer, 1980. — 374 p. This book contains the papers presented at the ICM2002 Satellite Conference on Nonlinear Evolution Equations and Dynamical Systems. About 50 mathematicians and scientists attended the meeting — including E. Witten (IAS), C. Nappi (Princeton), K. Khanin (Cambridge), D. Phong (Columbia), d'Hoker (UCLA) and Peng Chiakuei (CAS). The book covers several fields,...
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Mahwah: Psychology Press, 2007. — 148 p. — ISBN 9780805850123, 0805850120. Each volume in the Notre Dame Series on Quantitative Methodology features leading methodologists and substantive experts who provide instruction on innovative techniques designed to enhance quantitative skills in a substantive area. This latest volume focuses on the methodological issues and analyses...
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Springer, 2009. 198 p. ISBN 978-3-642-00936-5 Introduction Paradigm for Chaos Main Features of Chaotic Systems Reconstruction of Dynamical Systems Controlling Chaos Synchronization of Chaotic Systems Stochastic Resonance The Appearance of Regular Fluxes Without Gradients References Index
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2nd Edition. — Springer International Publishing, Switzerland, 2017. — 286 p. — (Understanding Complex Systems) — ISBN: 9783319424958 The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the...
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Springer, 2005 — 390 p. The notion of uniform hyperbolicity, introduced by Steve Smale in the early sixties, unified important developments and led to a remarkably successful theory for a large class of systems: uniformly hyperbolic systems often exhibit complicated evolution which, nevertheless, is now rather well understood, both geometrically and statistically. Another...
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2nd Edition. — Springer, 2016. — 471 p. — (Progress in Mathematics 318). — ISBN 3319338757. This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a...
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Cambridge University Press, 2000. — 417 Pages This book explores the exciting new field of complexity. It features in-depth coverage of important theoretical areas, including fractals, chaos, nonlinear dynamics, artificial life, and self organization. It also provides overviews of complexity in several applied areas, including parallel computation, control systems, neural...
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Cambridge University Press, 2014. — 434 p. — (Cambridge Studies in Advanced Mathematics 141) — ISBN: 1107042917 Since its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics, and it is essential background knowledge for any researcher in the field. In this comprehensive introduction the authors...
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Cambridge: Cambridge University Press, 2017. — 234 p. Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such...
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Cambridge University Press, 2002. — 250 p. — ISBN 0-521-80841-3. Examples and Basic Concepts Topological Dynamics Symbolic Dynamics Ergodic Theory Hyperbolic Dynamics Ergodicity of Anosov Diffeomorphisms Low-Dymensional Dynamics Complex Dynamics Measure-Theoretic Entropy
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CRC, 2017. — 400 s. — ISBN 978-1-4987-5596-2. This book covers the development of methods for detection and estimation of changes in complex systems. These systems are generally described by nonstationary stochastic models, which comprise both static and dynamic regimes, linear and nonlinear dynamics, and constant and time-variant structures of such systems. It covers both...
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Springer, 2011. — xvi;313 p. — ISBN 978-1-4419-6869-2 (Print) 978-1-4419-6870-8 (Online). Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices...
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3rd edition. — Springer International Publishing Switzerland, 2016. — 645 p. Impulsive Dynamics and Measure Differential Equations Impulsive Forces Measure Differential Equations (MDEs) Systems Subject to Unilateral Constraints Changes of Coordinates in MDEs Viscoelastic Contact/Impact Rheological Models Simple Examples Viscoelastic Contact Models and Restitution Coefficients...
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Basel: Birkhäuser, 1997. — 138 p. This book grew out of the work developed at the University of Warwick, under the supervision of Ian Stewart, which formed the core of my Ph.D. Thesis. Most of the results described were obtained in joint work with Ian; as usual under these circumstances, many have been published in research journals over the last two years. Part of Chapter 3 was...
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Princeton University, UK, 2003. — 180 p. — (Princeton Series in Applied Mathematics) — ISBN-10 0691112983. Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are...
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  • 1,87 МБ
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American Mathematical Society, 2000. — 398 p. — (Graduate Studies in Mathematics 23) — ISBN 0821808095. This is the first of two volumes on the qualitative theory of foliations. This volume is divided into three parts. It is extensively illustrated throughout and provides a large number of examples. Part 1 is intended as a "primer" in foliation theory. A working knowledge of...
  • №71
  • 4,91 МБ
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American Mathematical Society, 2003. — 539 p. — (Graduate Studies in Mathematics 60) — ISBN 0821808818. This is the second of two volumes on the qualitative theory of foliations. For this volume, the authors have selected three special topics: analysis on foliated spaces, characteristic classes of foliations, and foliated manifolds. Each of these is an example of deep interaction...
  • №72
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New York: Springer, 2017. — 266 p. This is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in...
  • №73
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Springer-Verlag, 1993. - 201 pages. ISBN: 0387979425, 3540979425 A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary...
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Cambridge: Cambridge University Press, 2017. — 574 p. This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about...
  • №75
  • 2,28 МБ
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Springer, 1981. - 142 pages. These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is...
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  • 671,27 КБ
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Springer, 2018. —239 p. — (Probability Theory and Stochastic Modelling 90). — ISBN 978-1-4939-8833-4. This book undertakes a detailed construction of Dynamic Markov Bridges using a combination of theory and real-world applications to drive home important concepts and methodologies. In Part I, theory is developed using tools from stochastic filtering, partial differential...
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  • 2,38 МБ
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World Scientific Publishing Company, 2004. - 528 pages. The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations. This engaging volume presents an authoritative overview of both autonomous and non-autonomous dynamical systems, including the global compact attractor. From an in-depth introduction to...
  • №78
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Singapore: World Scientific, 2007. — 598 p. This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a...
  • №79
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Singapore: World Scientific, 2009. — 357 p. Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered...
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Singapore: World Scientific, 2011. — 405 p. Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing...
  • №81
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Singapore: World Scientific, 2002. — 112 p. This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, or truth table, onto the point attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The...
  • №82
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Харьков: Аста, 2002. — 418 с. — ISBN 966-7021-64-5, 966-7021-20-3. This book provides an exhaustive introduction to the scope of main ideas and methods of the theory of infinite-dimensional dissipative dynamical systems which has been rapidly developing in recent years. In the examples systems generated by nonlinear partial differential equations arising in the different...
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Springer, 1999. — 219 p. This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented...
  • №84
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N.-Y.: AMS, 2014. - 303p. This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝd and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is...
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Springer London, 2016. — 192 p. — (Universitext). — ISBN 144717285X. This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as...
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  • 3,39 МБ
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Springer, 1999. — 457 p. — ISBN: 0387985123, 978-0387985121. This volume gives an account of new and recent developments in the theory of random and, in particular, stochastic dynamical systems. Its purpose is to document and, to some extent, summarise the current state of the field of random dynamical systems beyond the recent monograph, "Random Dynamical Systems" by Ludwig...
  • №87
  • 8,79 МБ
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World Scientific, 2010. — 421 p. This book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth...
  • №88
  • 5,43 МБ
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World Scientific Pub Co Inc, 2004. — 572 p. — ISBN-10 9810230516. The book comprises a broad panorama of phenomena occurring in four major classes of radiophysical and mechanical systems - linear, nonlinear, parametric, and nonlinear-parametric. An analytical technique for the broad circle of issues under consideration is developed. It is presented in a user-friendly form,...
  • №89
  • 34,45 МБ
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Springer, 2000. — 304 Pages. — ISBN: 3540521186 Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common...
  • №90
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Perseus Books, 1992. — 320 p. — ISBN: 0201554062 A First Course in Chaotic Dynamical Systems: Theory and Experiment is the first book to introduce modern topics in dynamical systems at the undergraduate level. Accessible to readers with only a background in calculus, the book integrates both theory and computer experiments into its coverage of contemporary ideas in dynamics....
  • №91
  • 12,17 МБ
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Westview Press, 1989. — 360 p. The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text,...
  • №92
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Springer-Verlag London Limited, 2008 — 496 p. Editors: S.S. Antman, J.E. Marsden, L. Sirovich. Many dynamical systems that occur naturally in the description of physical processes are piecewise-smooth. That is, their motion is characterized by periods of smooth evolutions interrupted by instantaneous events. Traditional analysis of dynamical systems has restricted its attention to...
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  • 73,78 МБ
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B.: Springer, 2009. - 270p. Part of Tsinghua University Texts, "Statistical Properties of Deterministic Systems" discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two problems related to the dynamical system are studied: first the...
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  • 1,32 МБ
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World Scientific Publishing Company, 2006. — 356 p. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J.E. Marsden,...
  • №95
  • 39,06 МБ
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Cambridge University Press, 2011. — 404 p. — (New Mathematical Monographs: 18). This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger...
  • №96
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Basel: Birkauser, 2011. — 293 p. — ISBN 978-3-0348-0014-3; e-ISBN 978-3-0348-0015-0 Поризм Понселе — классическая теорема проективной геометрии. Она и ее многомерные обобщения, сформулированные Дарбу, тесно связаны с теорией динамических систем (интегрируемые биллиарды на конфокальном пучке квадрик) и алгебраической геометрией (теоремы сложения на гиперэллиптических якобианах)....
  • №97
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New York: Springer, 2016. — 229 p. Guides the reader from the control of simple dynamical systems to real-world experiments assisted by ample supplementary material Contains interviews with leading experts in the field Offers extensive color figures with clear explanations Includes exercises at the end of every chapter and Matlab codes for all examples This is the first textbook...
  • №98
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Reviews of Modern Physics, Vol.57. Differentiable Dynamics and the Reconstruction of Dynamics from an Experimental Signal, Characteristic Exponents, Entropy and Information Dimension, Experimental Aspects.
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New York: Springer, 2018. — 320 p. The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of...
  • №100
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Springer, 2005. — 152 p. Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these...
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  • 2,11 МБ
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London: Springer, 2011. — 497 p. This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include...
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Springer Cham, Heidelberg, New York, Dordrecht, London, 2015. — 630 p. — (Graduate Texts in Mathematics 272) — ISBN 3319168975. Stunning recent results by Host-Kra, Green-Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern...
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1995-99 by Glenn Elert - 109 стр. Mathematical Experiments. Iterations & Orbits. Orbits & Bifurcations. Universality. Strange & Complex. Strange Attractors. Julia Sets. Mandelbrot Sets. What is Dimension? General Dimension. Topological Dimension. Fractal Dimension. Measuring Chaos. Harmonic Oscillator. Logistic Equation. Lyapunov Exponent. Lyapunov...
  • №104
  • 671,18 КБ
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London, Institute of Physics Publishing, 2003 - 327 стр. Microscopic Dynamics of Plasmas and Chaos discusses the resonant wave-particle interaction in plasmas, provides the tools for chaotic Hamiltonian dynamics, and describes a turbulent macroscopic system through the chaotic classical mechanics of the corresponding N-body problem. The book begins with the fundamentals of N-body...
  • №105
  • 2,86 МБ
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Springer, 2010. - 382 pages. Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather...
  • №106
  • 13,84 МБ
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UC Berkeley, 2006. — 139 pages. These notes survey, without too many precise details, the basic theory of probability, random differential equations and some applications. A really careful treatment assumes the students' familiarity with probability theory, measure theory, ordinary differential equations, and partial differential equations as well. The author tried to design...
  • №107
  • 1,28 МБ
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Academic Press, 2016. — 248 p. — ISBN 978-0-12-804294-6. Poincare-Andronov-Melnikov Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switching boundaries. Furthermore, bifurcations of...
  • №108
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Springer, 2011. - 390 pages. "Bifurcation and Chaos in Discontinuous and Continuous Systems" provides rigorous mathematical functional-analytical tools for handling chaotic bifurcations along with precise and complete proofs together with concrete applications presented by many stimulating and illustrating examples. A broad variety of nonlinear problems are studied involving...
  • №109
  • 2,59 МБ
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Springer, 2005. — 367 p. — ISBN 3540281150. "Nonlinear Oscillations in Mechanical Engineering" explores the effects of nonlinearities encountered in applications in that field. Since the nonlinearities are caused, first of all, by contacts between different mechanical parts, the main part of this book is devoted to oscillations in mechanical systems with discontinuities caused...
  • №110
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Springer, 2017. — 351 p. Introduction Global Warming and Climate Change Systems Theory Dynamic Systems Linear Systems Nonlinear Dynamic Systems: Uncoupled Nonlinear Dynamic Systems: Coupled Spatial Systems Power Laws and Non-Gaussian Systems Complex Systems Observationand Inference Water Concluding Thoughts
  • №111
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Springer International Publishing, Switzerland, 2016. – 323. – ISBN-10: 331930612X Includes the latest scientific developments in Multibody Dynamics State of the Art in this field Reflects the multidisciplinary character of the field This book includes selected papers from the ECCOMAS Thematic Conference on Multibody Dynamics, that took place in Barcelona, Spain, from June...
  • №112
  • 17,36 МБ
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World Scientific Publishing, 2015. — 564 p. — Volume 1 of Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications. This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists,...
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  • 42,53 МБ
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Springer, 2018. — 381 p. — (Pathways in Mathematics). — ISBN 978-3-319-72277-1. The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from...
  • №114
  • 4,81 МБ
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Springer, 2000. - 498 p. - The theory of stochastic processes provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. Noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for as yet open problems (information transmission in the nervous system and information processing in the brain, processes...
  • №115
  • 25,09 МБ
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Springer, 2013. - 236 p. - With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as...
  • №116
  • 10,41 МБ
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Springer, 2013. - 250 pages. ISBN: 3642335519 With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex...
  • №117
  • 10,17 МБ
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Singapore: World Scientific Pub Co Inc, 2000. — (Advanced Series in Nonlinear Dynamics: Volume 14). — 342 p. — ISBN: 978-9810241483. This book provides a thorough review of a class of powerful algorithms for the numerical analysis of complex time series data which were obtained from dynamical systems. These algorithms are based on the concept of state space representations of...
  • №118
  • 27,00 МБ
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Springer, 2007. - 303 pp. This volume reviews the current understanding of the Fermi-Pasta-Ulam (FPU) Problem without trying to force coherence on differing perspectives on the same problem by various groups or approaches. The contributions lead the interested but inexperienced reader through gradual understanding, starting from general analysis and proceeding towards more...
  • №119
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Springer, 2011, 231 p. Wavelets: Theory and Applications for Manufacturing presents a systematic description of the fundamentals of wavelet transform and its applications. Given the widespread utilization of rotating machines in modern manufacturing and the increasing need for condition-based, as opposed to fix-interval, intelligent maintenance to minimize machine down time and...
  • №120
  • 4,13 МБ
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Publisher: arXiv, 2011. - 150 pages. The goal of this set of lectures is to combine two seemingly unrelated topics: - The study of Boolean functions, a field particularly active in computer science; - Some models in statistical physics, mostly percolation. The link between these two fields can be loosely explained as follows: a percolation configuration is built out of...
  • №121
  • 1,38 МБ
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Springer International Publishing AG, 2018. — 364 p. — ISBN 3319739530. Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on...
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2nd Edition. — Springer International Publishing, Switzerland, 2017. — 304 p. — ISBN-10: 3319439421 After spending many years as a systems engineer for controlling various production processes, I began to view the world more and more as a collection of systems. In my engineering work, systems existed as manufacturing entities, such as chemical plants, oil refineries, food and...
  • №123
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2nd edition. — New York: Springer, 2016. — 304 p. Apply system knowledge at work and in daily life without deep mathematical knowledge Build models and simulate system behaviors on a personal computer Optimize systems in many different ways Reduce or eliminate unintended consequences Develop a holistic world view Systems are everywhere and we are surrounded by them. We are...
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  • 4,80 МБ
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Springer, 2015. - 239 pp. This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic...
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  • 9,35 МБ
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Springer, 2009. — 288 p. Papers in this collection partly represent the set of talks that were presented at Texas Tech University on the occasion of Daya’s memorial workshop in the year 2007. Daya had a varied interest in the field of Dynamics and Control Theory and the papers bring out the essence of his involvement in these activities. He also had a large number of...
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  • 4,67 МБ
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Springer, 1997. — 217 p. The closed orbits of three-dimensional flows form knots and links. This book develops the tools - template theory and symbolic dynamics - needed for studying knotted orbits. This theory is applied to the problems of understanding local and global bifurcations, as well as the embedding data of orbits in Morse-Smale, Smale, and integrable Hamiltonian flows....
  • №127
  • 1,66 МБ
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Springer International Publishing Switzerland 2015. — 219 p. — (Nonlinear Systems and Complexity 11). — ISBN: 978-3-319-09866-1 (Print) 978-3-319-09867-8 (Online). This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to...
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  • 3,01 МБ
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N.-Y.: Springer, 2015. - 240p. This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The...
  • №129
  • 11,50 МБ
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Springer International Publishing, Switzerland, 2016. — 313 p. — (Developments in Mathematics) — ISBN: 3319448463. This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results...
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4th edition. — Cham; Heidelberg; New York; Dordrecht; London: Springer, 2015. — XVI, 422 p. — ISBN 978-3-319-16264-5; ISBN 978-3-319-16265-2 (eBook). This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are...
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Springer, 2010. - 325 pages. Discover a wide range of findings in quantitative complex system science that help us make sense of our complex world. Written at an introductory level, the book provides an accessible entry into this fascinating and vitally important subject.
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Proceedings of the NATO Advanced Study Institute held at the University of Warwick, Coventry, England, 27 August–6 September, 1974 -312 c. The first international conference on differential games was held at Amherst, Massachusetts, in September 1969. Asecond meeting, partially supported by N.A.T.O., was held in Varenna, Italy, in June 1970. At these conferences many new...
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  • 12,04 МБ
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Berlin, Springer, 2003. — 343 p. Chaos control refers to purposefully manipulating chaotic dynamical behaviors of some complex nonlinear systems. As a new and young discipline, chaos control has in effect come into play with many traditional scientific and technological advances today. Automatic control theory and practice, on the other hand, is a traditional and long-lasting...
  • №134
  • 14,23 МБ
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Springer, 1983. — 471 p. This book applied the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking the cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer...
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Providence: American Mathematical Society. 2012. — 322 p. This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9–10, 2013, in San Diego, CA. Included are papers on design and analysis of discrete-time and continuous-time dynamical systems...
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Springer International Publishing AG, part of Springer Nature, 2017. — 411 p. — (Springer Proceedings in Mathematics & Statistics 205) — ISBN 978-3-319-64172-0. Dynamical systems as a field have had tremendous impact across mathematics and the sciences that goes far beyond the in-depth study and classification of the qualitative behavior of flows and terations. The...
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Springer International Publishing AG, part of Springer Nature, 2017. — 411 p. — (Springer Proceedings in Mathematics & Statistics 205) – ISBN 978-3-319-64172-0. Dynamical systems as a field have had tremendous impact across mathematics and the sciences that goes far beyond the in-depth study and classification of the qualitative behavior of flows and terations. The...
  • №138
  • 6,49 МБ
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Princeton University Press, 2008. — 976 p. Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed...
  • №139
  • 6,07 МБ
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A Macroscopic Approach to Complex System Germany, Springer, 2000 - 232 p. This book presents the concepts needed to deal with self-organizing complex systems from a unifying point of view that uses macroscopic data. The various meanings of the concept "information" are discussed and a general formulation of the maximum information (entropy) principle is used. With the aid of...
  • №140
  • 2,00 МБ
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Dover Publications, 2015. — 180 p. By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and...
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Springer, 1991. — 581 p. The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps...
  • №142
  • 8,18 МБ
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Springer, 1991. — 577 p. — (Texts in Applied Mathematics 3) — ISBN 1461287650. The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once...
  • №143
  • 48,42 МБ
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Springer, 2002. - 293 pages. From the reviews of the second edition: "This book presents a contemporary geometric theory of infinite-dimensional dynamical systems where the major emphasis is on retarded functional-differential equations. … Each chapter contains some abstract theorems but the authors give some examples as well illustrating these general results and having...
  • №144
  • 2,13 МБ
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Springer, 1999. — 430 p. — (Applied Mathematical Sciences, 138). — ISBN 0-387-98697-9. Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled with instabilities, can result in highly irregular behavior. This book gives a unified treatment of resonant...
  • №145
  • 4,12 МБ
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Springer International Publishing AG, 2017. — 121 p. — (SpringerBriefs in Mathematics) — ISBN 978-3-319-61933-0. Numerical dynamics is concerned with how well a numerical scheme applied to a differential equation replicates the dynamical behaviour of the dynamical system generated by the differential equation, in particular its long-term or asymptotic behaviour. This essentially...
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Springer, 2010. - 340 pages. ISBN: 0857291114 An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and...
  • №147
  • 3,19 МБ
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Elsevier, 2010. - 560 Pages. In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent...
  • №148
  • 6,81 МБ
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Princeton: Princeton University Press, 1986. - 410p. This book offers a fundamental explanation of nonlinear oscillations in physical systems. Originally intended for electrical engineers, it remains an important reference for the increasing numbers of researchers studying nonlinear phenomena in physics, chemical engineering, biology, medicine, and other fields.
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New York: AMS, 2014. - 209p. Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology. This book presents a mathematical approach to stochastic resonance which is based on a large deviations principle (LDP) for randomly perturbed dynamical systems with a weak inhomogeneity given...
  • №150
  • 1,62 МБ
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Oxford University Press, 2014. — 112 p. — (Very Short Introductions). The importance of complexity is well-captured by Hawking's comment: "Complexity is the science of the 21st century". From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly influential...
  • №151
  • 559,21 КБ
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Springer-Verlag Berlin, 2006, 318 pages This classic text, an often-requested reprint, develops and explains the foundations of noise-induced processes. At its core is a self-contained, textbook-style presentation of the elements of probability theory, of the theory of Markovian diffusion processes and of the theory of stochastic differential equations, on which the modeling...
  • №152
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Монография, Springer, London, 2009, 357р. Today, chaos is no longer a stranger to many. Instead, chaos theory and technology. have gradually become well known as a promising research field with significant. mpacts on an increasing number of novel, potentially attractive, time- and energycritical engineering applications. Contents. Overview. The Origin and Development of...
  • №153
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Monograph. — Springer, 2009. — 297 p. Vibro-impact dynamics has occupied a wide spectrum of studies by dynamicists, physicists, and mathematicians. These studies may be classified into three main categories: modeling, mapping and applications. The main techniques used in modeling of vibro-impact systems such as phenomenological modelings, Hertzian models, and non-smooth...
  • №154
  • 4,69 МБ
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Springer-Verlag New York 2010. — 2nd Ed. — (Applied Mathematical Sciences 149). — 520 pp. — ISBN: 978-1-4419-7075-6 (Print) 978-1-4419-7296-5 (Online). This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods - based on asymptotic, probabilistic, and group-theoretic standpoints - are used to examine...
  • №155
  • 10,51 МБ
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Springer, 2009. — 490 pages. ISBN: 3540856315 This edited book is aimed at interdisciplinary device-oriented applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators,...
  • №156
  • 31,40 МБ
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New York: Springer, 2017. — 359 p. This volume collects contributions related to selected presentations from the 12th IFAC Workshop on Time Delay Systems, Ann Arbor, June 28-30, 2015. The included papers present novel techniques and new results of delayed dynamical systems. The topical spectrum covers control theory, numerical analysis, engineering and biological applications as...
  • №157
  • 14,52 МБ
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Springer-Verlag New York 2011. — (Applied Mathematical Sciences 178). — 174 pp. — ISBN: 978-1-4614-0334-0 (Print) 978-1-4614-0335-7 (Online). The book presents the recently introduced and already widely cited semi-discretization method for the stability analysis of delayed dynamical systems with parametric excitation. Delay-differential equations often come up in different...
  • №158
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New York: Springer, 2010. - 307 p. This book is devoted to complexity understanding and management, considered as the main source of efficiency and prosperity for the next decades. Divided into six chapters, the book begins with a presentation of basic concepts as complexity, emergence and closure. The second chapter looks to methods and introduces polystochastic models, the wave...
  • №159
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N.-Y.: Springer, 2008. - 844p. Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on...
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  • 27,28 МБ
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New York: Springer, 2006. — 841 p. This volume presents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures. By "complex systems", in this book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a unified geometrical approach to dynamics of complex systems of...
  • №161
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Hoboken: CRC Press, 2013. — 363 p. Preface Authors Introduction to Mathematical Modeling Modeling of Systems from Natural Science Introduction to Chaotic Dynamics Chaotic Dynamics in Model Systems from Natural Science Modeling of Some Engineering Systems Solutions to Odd-Numbered Problems
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Springer, 2014. — 430 pages. ISBN: 1461468760. Nonlinear Approaches in Engineering Applications 2 focuses on the application of nonlinear approaches to different engineering and science problems. The selection of the topics for this book is based on the best papers presented in the ASME 2010 and 2011 in the tracks of Dynamic Systems and Control, Optimal Approaches in Nonlinear...
  • №163
  • 12,16 МБ
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Springer, 2018. — 531 p. — ISBN 978-3-030-02106-1. The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to...
  • №164
  • 19,31 МБ
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New York: Springer, 2016. — 515 p. This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory...
  • №165
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New York: ITAe, 2011. - 537p. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. The contribution of the book enlarges the field of the Discrete-Time Systems with...
  • №166
  • 4,24 МБ
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Cambridge University Press, 2010. — 182 p. — (Cambridge Studies in Advanced Mathematics 122) — ISBN 978-0-521-19440-2. This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory,...
  • №167
  • 1,31 МБ
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2nd edition. — Cambridge University Press, 2003. — 388 p. — ISBN: 0521821509 The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be...
  • №168
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2 edition. — Cambridge University Press, 2003. — 388 p. — ISBN: 0521821509 The time variability of many natural and social phenomena is not well described by standard methods of data analysis. However, nonlinear time series analysis uses chaos theory and nonlinear dynamics to understand seemingly unpredictable behavior. The results are applied to real data from physics,...
  • №169
  • 36,41 МБ
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Academic Press, 1996. — 164 p. — ISBN 9780123968401, 0123968402. More than two decades of intensive studies on non-linear dynamics have raised questions on the practical applications of chaos. One possible answer is to control chaotic behavior in a predictable way. This book, oneof the first on the subject, explores the ideas behind controlling chaos. The book explains, using...
  • №170
  • 15,86 МБ
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New York: Springer, 1995. — 437 p. Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment...
  • №171
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Basel: Birkhäuser, 2000. — 278 p. This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type"...
  • №172
  • 9,16 МБ
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Cambridge: Cambridge University Press, 1996. — 824 p. This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental...
  • №173
  • 80,45 МБ
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World Scientific, 1984. — 252 p. This publication collates the lectures and papers delivered at the meeting on "The theory of dynamical systems and its applications to nonlinear problems" held at the Research Institute for Mathematical Sciences of Kyoto University in Kyoto, Japan, from July 4 to 7, 1984. The twenty lectures are classified into four groups: dynamical systems,...
  • №174
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Springer International Publishing, Switzerland, 2013. — 290 p. — (Lecture Notes in Mathematics 2089) — ISBN: 3319012878 This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one...
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  • 3,52 МБ
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American Mathematical Society, 2010. — 245 p. — (Mathematical Surveys and Monographs). — ISBN 0821848941. The original motivation for this work came from the study of certain results in ergodic theory, primarily, but not exclusively, obtained over the last several years. These included: i) Work of Hjorth and Foreman-Weiss concerning the complexity of the problem of classification...
  • №176
  • 1,20 МБ
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Springer Netherlands, 1994. — XVI, 672 p. — (An International Book Series on The Fundamental Theories of Physics, v. 61). This monograph is devoted to an entirely new branch of nonlinear physics – solitary intrinsic states, or autosolitons, which form in a broad class of physical, chemical and biological dissipative systems. Autosolitons are often observed as highly nonequilibrium...
  • №177
  • 17,80 МБ
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New York: Springer, 2017. — 455 p. This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing,...
  • №178
  • 4,17 МБ
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Springer, 2016. — 521 p. The book is the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Oscillations Nonlinear Simulation Using Harmonic Balance Nonlinear Modal...
  • №179
  • 37,72 МБ
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Springer, 2016. — 414 p. Nonlinear Dynamics, Volume 1. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the first volume of ten from the Conference, brings together contributions to this important area of research and engineering. Th e collection presents early findings and case studies...
  • №180
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Springer, 2017. — 220 p. Nonlinear Dynamics, Volume 1: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the first volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics,...
  • №181
  • 16,46 МБ
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Springer, 2019. — 421 p. Nonlinear Dynamics, Volume 1: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the first volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics,...
  • №182
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Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014. — Springer Cham Heidelberg New York Dordrecht London, 2014, VIII, 319 p. 256 illus., 208 illus. — ISBN 978-3-319-04521-4, ISBN 978-3-319-04522-1 (eBook), DOI 10.1007/978-3-319-04522-1in color. — (Conference Proceedings of the Society for Experimental Mechanics Series). This critical...
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Kevin M. Pilgrim - Combinations of Complex Dynamical Systems (Lecture Notes in Mathematics). Springer. 2003, 120 pages. The goal of this research monograph is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain...
  • №184
  • 1,23 МБ
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3rd edition. — Pearson, 2001. — 750 p. This text is intended for a first-year graduate-level course on nonlinear systems or control. It may also be used for self study or reference by engineers and applied mathematicians. It is an outgrowth of my experience teaching the nonlinear systems course at Michigan State University, East Lansing. Students taking this course have had...
  • №185
  • 17,09 МБ
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3rd edition. — Pearson, 2001. — 241 p. This text is intended for a first-year graduate-level course on nonlinear systems or control. It may also be used for self study or reference by engineers and applied mathematicians. It is an outgrowth of my experience teaching the nonlinear systems course at Michigan State University, East Lansing. Students taking this course have had...
  • №186
  • 22,42 МБ
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New York: Springer, 2004. — 278 p. Contents : Front Matter On Applications of P -Adic Analysis P -Adic Numbers and P -Adic Analysis P -Adic Dynamical Systems Perturbation of Monomial Systems Dynamical Systems in Finite Extensions of ℚ p Conjugate Maps P -Adic Ergodicity P -Adic Neural Networks Dynamics in Ultra-Pseudometric Spaces Random Dynamics Dynamics of Probability...
  • №187
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Springer-Verlag New York 2012. — 2nd Ed. — (Applied Mathematical Sciences 156). — 400 pp. — ISBN: 978-1-4614-0501-6 (Print) 978-1-4614-0502-3 (Online). In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as...
  • №188
  • 2,68 МБ
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Springer, 1987. — 457 p. The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study...
  • №189
  • 3,09 МБ
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New York: Springer, 1997. - 254p. Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined...
  • №190
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World Scientific Publishing, 2012. — 400 pages. — ISBN-10: 9814340588 This volume provides the latest developments in the field of fractional dynamics, which cover fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important...
  • №191
  • 6,01 МБ
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Hoboken: Wiley, 2015. — 499 p. Craig Kluever 'sDynamic Systems: Modeling, Simulation, and Control highlights essential topics such as analysis, design, and control of physical engineering systems, often composed of interacting mechanical, electrical and fluid subsystem components. The major topics covered in this text include mathematical modeling, system-response analysis, and an...
  • №192
  • 5,83 МБ
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Birkhauser, 1997. — 107 p. DMV Seminar Oberwolfach July 21-27 1996. Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin­ tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase...
  • №193
  • 629,82 КБ
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New York: Springer, 2002. — 428 p. The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex­ panded...
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Wiley, 2011. - 386 pages. The Duffing Equation: Nonlinear Oscillators and their Behaviour brings together the results of a wealth of disseminated research literature on the Duffing equation, a key engineering model with a vast number of applications in science and engineering, summarizing the findings of this research. Each chapter is written by an expert contributor in the...
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  • 15,56 МБ
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Amsterdam: De Gruyter , 2015. - 348p. This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds...
  • №196
  • 3,48 МБ
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European Mathematical Society, Switzerland, 2012. — 487 p. — (EMS Monographs in Mathematics) — ISBN-10: 3037191066 Wave maps are the simplest wave equations taking their values in a Riemannian manifold $(M,g)$. Their Lagrangian is the same as for the scalar equation, the only difference being that lengths are measured with respect to the metric $g$. By Noether's theorem,...
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Springer, 1994, — 428 p. Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the...
  • №198
  • 16,71 МБ
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Springer, 2015. — 814 p. — (Applied Mathematical Sciences). — ISBN: 3319123157, 9783319123158. This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and...
  • №199
  • 15,02 МБ
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London: King's College, 2005. — 138 p. The present course is about dynamical systems i.e. systems described by a set of n variables {x1,... ,xn}, each depending on time t, governed by dynamical laws given in terms of ODEs of the form d/ dt xi = fi(t,x1,... ,xn) i = 1,... ,n . (1) We shall learn about methods to analyse such systems. Available methods can generally be classified as...
  • №200
  • 907,22 КБ
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Chapman & Hall/CRC, 2004. - 360 pages. Following the work of Yorke and Li in 1975, the theory of discrete dynamical systems and difference equations developed rapidly. The applications of difference equations also grew rapidly, especially with the introduction of graphical-interface software that can plot trajectories, calculate Lyapunov exponents, plot bifurcation diagrams,...
  • №201
  • 13,08 МБ
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(Progress in Systems and Control Theory. Volume 17). New York: Springer Science+Business Media, 1993. – 276 p. Assembles papers on recent Russian research in these fields, with special emphasis on the treatment of uncertain systems in a deterministic setting. Coverage spans the three main branches of uncertain dynamics – differential games; evolution, estimation and control; and...
  • №202
  • 5,60 МБ
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Springer, 2004. — 634 p. — (Applied Mathematical Sciences Volume 112). — ISBN 978-1-4419-1951-9. This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special...
  • №203
  • 51,08 МБ
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New York: Springer, 2018. — 366 p. This book focuses on modelling and simulation, control and optimization, signal processing, and forecasting in selected nonlinear dynamical systems, presenting both literature reviews and novel concepts. It develops analytical or numerical approaches, which are simple to use, robust, stable, flexible and universally applicable to the analysis of...
  • №204
  • 12,72 МБ
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Berlin: Springer, 2003. - 627 p. Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who...
  • №205
  • 14,39 МБ
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N.-Y.: Springer, 2010. - 332p. Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularlysuitable tools for...
  • №206
  • 13,64 МБ
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Berlin: Springer, 2001. — 400 p. In the present book the modern theory of non-linear oscilla- tions both regular and chaotic, is set out, primarily, as applied to mechanical problems. The material is presented in a non-traditional manner with emphasizing of the new results of the theory otained partially by the author, who is one of the leading experts in the area. Among the...
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  • 13,15 МБ
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New York: Springer, 2018. — 267 p. Hybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system...
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  • 5,08 МБ
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New York: ITexLi, 2016. — 357 p. This volume is dedicated to nonlinear systems in various fields, and consists of two parts. The book consists mainly of two parts. First. Chapter 1 and Chapter 2 treat design techniques based on linearization of nonlinear systems. An analysis of nonlinear system over quantum mechanics is discussed in Chapter 3. Chapter 4 to Chapter 7 are...
  • №209
  • 10,43 МБ
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Springer International Publishing AG, 2018. — 561 p. — (Interaction of Mechanics and Mathematics) — ISBN 978-3-319-56951-2. This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches...
  • №210
  • 6,39 МБ
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Springer, 2004. — 236 p. — (Lecture Notes in Applied and Computational Mechanics Volume 18). — ISBN 978-3-642-06029-8. This monograph combines the knowledge of both the field of Nonlinear Dynamcis and Non-smooth Mechanics and presents a framework for a class of non-smooth mechanical systems using techniques from both fields. During the last decades, the Non-smooth Mechanics...
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  • 2,78 МБ
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Amsterdam: Springer, 1996. — 414 p. This book is devoted to nonlocal theory of nonlinear oscillations. The frequency methods of investigating problems of cycle existence in multidimensional analogues of Van der Pol equation, in dynamical systems with cylindrical phase space and dynamical systems satisfying Routh-Hurwitz generalized conditions are systematically presented here for...
  • №212
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N.-Y.: Springer, 2005. - 300p. The application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering...
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Amsterdam: Springer, 2011. - 175p. The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst,...
  • №214
  • 2,88 МБ
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New York: Atlantis Press, 2017. — 190 p. Thurston maps are topological generalizations of postcritically-finite rational maps. This book provides a comprehensive study of ergodic theory of expanding Thurston maps, focusing on the measure of maximal entropy, as well as a more general class of invariant measures, called equilibrium states, and certain weak expansion properties of...
  • №215
  • 3,27 МБ
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N.-Y.: Springer, 2015. — 158 p. Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in dynamical systems. Although the methods and concepts are briefly introduced, a prior knowledge of center-manifold reductions and normal-form...
  • №216
  • 3,21 МБ
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Springer, 2013. — 226 p. — (Springer Series in Synergetics). — ISBN 3642312500. Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field...
  • №217
  • 10,34 МБ
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World Scientific Publishing Co. Pte. Ltd.,2009. - 270 pp. The objective of this book is to review the state-of-the-art chaos control methods for some common nonlinear circuits and systems, such as electronic circuits, power converters, human brains, phase lock loops, sigma delta modulators, etc. and stimulate further research and development in chaos control for nonlinear...
  • №218
  • 25,76 МБ
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John Wiley & Sons Ltd, 1997. — 350 p. — (Pure and Applied Mathematics) — ISBN-10: 0471967920 This book presents the central issues and emphasizes comparison, assessment and how to combine method and application. It reviews different approaches to guide researchers to appropriate classes of techniques. Includes exercises and solutions and gives an itinerary for readers...
  • №219
  • 25,34 МБ
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Berlin: Springer, 2012. — 220 p. "Pseudochaotic Kicked Oscillators: Renormalization, Symbolic Dynamics, and Transport" presents recent developments in pseudochaos, which is concerned with complex branching behaviors of dynamical systems at the interface between orderly and chaotic motion. Pseudochaos is characterized by the trapping of orbits in the vicinity of self-similar...
  • №220
  • 4,39 МБ
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Hoboken: Wiley, 2016. — 312 p. Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines...
  • №221
  • 4,71 МБ
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Springer-Verlag, Berlin, Heidelberg, 2016. – 365 p. – ISBN-10: 3662490765 The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications...
  • №222
  • 12,40 МБ
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Springer, 2012. - 507 pages. This volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the...
  • №223
  • 9,96 МБ
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Springer, 2013. - 239 pp. Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques...
  • №224
  • 4,73 МБ
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Higher Education Press, Beijing and Springer-Verlag, Berlin, 2010, 386 pages "Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics...
  • №225
  • 15,77 МБ
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New York: Springer, 2012. - 498 p. Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent...
  • №226
  • 13,18 МБ
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Springer-Verlag Berlin Heidelberg 2010. — 311 p. — (Nonlinear Physical Science). — ISBN: 978-3-642-12342-9 (Print) 978-3-642-12343-6 (Online). In memory of Dr. George Zaslavsky, "Long-range Interactions, Stochasticity and Fractional Dynamics" covers the recent developments of long-range interaction, fractional dynamics, brain dynamics and stochastic theory of turbulence, each...
  • №227
  • 10,32 МБ
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Springer, 2016. — 205 p. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes. Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology. Introduces new concepts, methods, and applications in nonlinear dynamical...
  • №228
  • 3,27 МБ
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Springer, 2017. — 307 p. — (Nonlinear Systems and Complexity). — ISBN 10 3319427776. This book examines discrete dynamical systems with memory-nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses...
  • №229
  • 8,83 МБ
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Basel: Birkhäuser, 2018. — 666 p. — ISBN 9783319781440, 3319781448. This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary...
  • №230
  • 18,28 МБ
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World Scientific Publishing, Singapore, 2005, 375 pages, ISBN 981-256-287-7. This book provides an introduction to a newly developed bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering. The first two chapters of the book contain a brief introduction to the standard bifurcation theory for nonlinear...
  • №231
  • 12,60 МБ
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Springer, 2019. — 232 p. — (Nonlinear Systems and Complexity 22). — ISBN 3319785117. This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry...
  • №232
  • 14,14 МБ
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Springer, 2019. — 232 p. — (Nonlinear Systems and Complexity 22). — ISBN 3319785117. This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry...
  • №233
  • 30,92 МБ
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Basel, Switzerland: MDPI, 2014. — 553 p. — ISBN 978-3-906980-52-2. Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and...
  • №234
  • 18,29 МБ
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Singapore: World Scientific Publishing Company, 2005. — 448 p. osmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are...
  • №235
  • 7,81 МБ
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New York: Springer, 2016. - 97 p. This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which...
  • №236
  • 1,87 МБ
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Springer, 2012. — 494 p. — (Fields Institute Communications 64). — ISBN 1461445221. This collection covers a wide range of topics of infinite dimensional dynamical systems generated by parabolic partial differential equations, hyperbolic partial differential equations, solitary equations, lattice differential equations, delay differential equations, and stochastic differential...
  • №237
  • 4,01 МБ
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New York: CRc Press LLC, 2016. - 338p. Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called...
  • №238
  • 9,85 МБ
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Springer, 2013. — 608 p. — ISBN-10: 1461434742 Advanced Dynamics: Analytical and Numerical Calculations with MATLAB provides a thorough, rigorous presentation of kinematics and dynamics while using MATLAB as an integrated tool to solve problems. Topics presented are explained thoroughly and directly,allowing fundamental principles to emerge through applications from areas such...
  • №239
  • 12,37 МБ
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Springer, 2012. - 406 pages. This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called base functions. These are absolutely necessary to obtain the auxiliary functions involved in the...
  • №240
  • 3,88 МБ
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New York: Springer, 2014. — 143 p. The high reliability required in industrial processes has created the necessity of detecting abnormal conditions, called faults, while processes are operating. The term fault generically refers to any type of process degradation, or degradation in equipment performance because of changes in the process's physical characteristics, process...
  • №241
  • 4,51 МБ
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Boca Raton: CRC Press/Taylor & Francis Group, 2017. — 228 p. The investigation of nonlinear systems with a small parameter is attributable by a lot of modern problems of mechanics, physics, hydrodynamics, electrodynamics of charge-particle beams, space technology, astrodynamics and many others. The key problem in solution of various applied problems is that of the stability of...
  • №242
  • 1,58 МБ
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Cambridge, Cambridge University Press, 2001 - 309 стр. Statics and dynamics: some elementary concepts. Review of linear systems. Stability of fixed points. Invariant and attracting sets, periodic and quasiperiodic orbits. Local bifurcations. Chaotic sets and chaotic attractors. Characteristic exponents, fractals, homoclinic orbits. Transition to chaos. The ergodic...
  • №243
  • 1,45 МБ
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Taylor & Francis, 2001. — 256 p. This book presents a unified view of mathematical modelling, simulation and control for complex non-linear dynamical systems using soft computing techniques and fractal theory. Our particular point of view is that modelling, simulation and control are problems that can not be considered apart because they are intrinsically related in real-world...
  • №244
  • 8,89 МБ
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London: Springer-Verlag, 2011. — 340 p. — ISBN 978-0-85729-611-5; e-ISBN 978-0-85729-612-2 The goal of this book is to present several concepts useful for the analysis of dynamical systems, and to illustrate, in the last two chapters, how they can be actually applied to improve the state of the art for two classical topics in nonlinear systems theory: the linearization of a...
  • №245
  • 2,29 МБ
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New York: Springer, 2017. — 386 p. This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a...
  • №246
  • 4,16 МБ
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SpringerScience+Business Media, LLC., 2012. XXIX, 1858 p. — ISBN: 978-1-4614-1806-1. Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the...
  • №247
  • 70,29 МБ
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Springer, 1991. — 140 p. The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group (...
  • №248
  • 969,37 КБ
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Springer-Verlag New York 2015. — (Applied Mathematical Sciences 193). — 660 pp. — ISBN: 978-1-4939-2705-0 (Print) 978-1-4939-2706-7 (Online). This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully...
  • №249
  • 11,40 МБ
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New York, USA: Springer-Verlag, 2015. — 660 pp. — (Applied Mathematical Sciences 193).— ISBN-10 1493927051. This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract...
  • №250
  • 12,91 МБ
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Article from magazine: Physica 5D (1982) 370-382. North-Holland Publishing Company, - 17 стр. Dynamical systems with quasiperiodic behavior, i.e., two incommensurate frequencies, may be studied via discrete maps which show smooth continuous invariant curves with irrational winding numbers. In this paper these curves are followed using renormalization group techniques which are...
  • №251
  • 562,40 КБ
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New York: Springer, 2016. - 199 p. Focuses on the Bond Graph Method, a technique that covers interdisciplinary modeling problems Addresses how to use software, such as MATLAB and Simulink and 20-Sim, to use different modeling paradigms interchangeably Explains all analytical equations with different examples of electrical, mechanical, and mechatronics systems This book...
  • №252
  • 6,81 МБ
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Springer, 2006. — 249 p. The impact of Bénard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field. Introduction The Context of...
  • №253
  • 6,24 МБ
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Hindustan Book Agency, India, 2013. — 200 p. — (Texts and Readings in Mathematics 06) — ISBN 978-93-86279-53-8. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that the basic topics of Ergodic Theory such as the Poincare recurrence lemma, induced automorphisms and...
  • №254
  • 14,26 МБ
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New Delhi: Hindustan Book Agency, 1998. — 228 p. This book treats some basic topics in the spectral theory of dynamical systems, where by a dynamical system we mean a measure space on which a group of automorphisms acts preserving the sets of measure zero. The treatment is at a general level, but even here, two theorems which are not on the surface, one due to H. Helson and W....
  • №255
  • 1,95 МБ
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Wiley-VCH, 1993. — 536 p. Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises.
  • №256
  • 4,87 МБ
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Wiley-Interscience, 1973. - 425 pages. The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.
  • №257
  • 3,07 МБ
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Wiley, 1995. - 720 pages. Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems...
  • №258
  • 6,65 МБ
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American Mathematical Society, 2015. — 120 p. — (MEMOIRS of the American Mathematical Society Vol. 237, No.1122) — ISBN 1470415445. The author introduces a notion of hyperbolic groupoids, generalizing the notion of a Gromov hyperbolic group. Examples of hyperbolic groupoids include actions of Gromov hyperbolic groups on their boundaries, pseudogroups generated by expanding...
  • №259
  • 1022,03 КБ
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Cambridge University Press, 1995. — 263 p. One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications...
  • №260
  • 3,15 МБ
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World Scientific, 2007. — 343 p. Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from...
  • №261
  • 5,57 МБ
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European Mathematical Society, 2013. — 226 p. — (EMS Tracts in Mathematics 21). — ISBN 3037191244. In this book dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications. In the first...
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  • 2,57 МБ
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New York: Springer, 2017. - 490 p. This book presents the state-of-the-art in non-linear dynamics and sunspots. These two topics have been the core of an international conference on instability and public policies in a globalized world, organized at Aix-Marseille School of Economics and GREQAM in honor of Jean-Michel Grandmont. He has made significant contributions on general...
  • №263
  • 7,84 МБ
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Oxford: Oxford University, 2014. - 448 p. The best parts of physics are the last topics that our students ever see. These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many high-tech businesses. Topics such as traffic on the World Wide Web, the spread of epidemics through globally-mobile...
  • №264
  • 20,39 МБ
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6th Edition. — Springer, 2003. — 360 pages. — ISBN: 3540047581. This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start...
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  • 2,69 МБ
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World Scientific Publishing, 2018. — 271 p. — (World Scientific Series on Nonlinear Science Series A — Vol. 92). — ISBN 978-981-3225-28-2. This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original...
  • №266
  • 5,38 МБ
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New York: Springer, 2008. - 333p. Discontinuous Systems develops nonsmooth stability analysis and discontinuous control synthesis based on novel modeling of discontinuous dynamic systems, operating under uncertain conditions. While being primarily a research monograph devoted to the theory of discontinuous dynamic systems, no background in discontinuous systems is required;
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  • 7,48 МБ
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B.: Springer-Verlag, 2007. - 288p. Contents : Front Matter Introduction Symbolic Image Periodic Trajectories Newton's Method Invariant Sets Chain Recurrent Set Attractors Filtration Structural Graph Entropy Projective Space and Lyapunov Exponents Morse Spectrum Hyperbolicity and Structural Stability Controllability Invariant Manifolds Ikeda Mapping Dynamics...
  • №268
  • 15,63 МБ
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Cambridge, Cambridge University Press, 1988. Part I: Classical dynamics. Linear dynamics systems. Nonlinear systems. Chaotic motion. Normal forms. Maps of the cycle. Integrable and quasi-integrable systems. Part II: Quantum dynamycs. Torus quantization. Quantization of ergodic systems. Periodic orbits in quantum mechanics.
  • №269
  • 2,40 МБ
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Springer, 2013. — XVI, 356 p. — (Computational Methods in Applied Sciences Volume 26) — ISBN 978-94-007-5133-0, ISBN 978-94-007-5134-7 (eBook). The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and...
  • №270
  • 11,90 МБ
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Springer, 2011. — 342 p. At the dawn of the 21st century, computational stochastic dynamics is an emerging research frontier. This book focuses on advanced computational methods and software tools which can highly assist in tackling complex problems in stochastic dynamic/seismic analysis and design of structures. The book is primarily intended for researchers and post-graduate...
  • №271
  • 6,61 МБ
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New York: AMS, 2009. - 334p. Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets,...
  • №272
  • 4,23 МБ
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Cambridge University Press, 1995. — 445 p. Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence,...
  • №273
  • 2,49 МБ
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Springer, 2011. - 218 pages. "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution...
  • №274
  • 11,13 МБ
  • дата добавления неизвестна
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Springer International Publishing AG, 2018. — 497 p. — (Studies in Systems, Decision and Control 133). — ISBN 331971242X. This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with...
  • №275
  • 33,81 МБ
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Springer International Publishing AG, 2018. — 497 p. — (Studies in Systems, Decision and Control 133). — ISBN 331971242X. This book highlights the latest findings on nonlinear dynamical systems including two types of attractors: self-excited and hidden attractors. Further, it presents both theoretical and practical approaches to investigating nonlinear dynamical systems with...
  • №276
  • 13,72 МБ
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Cambridge University Press, 2001. — 433 p. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. The first half of this book describes synchronization without formulae,...
  • №277
  • 7,24 МБ
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Springer, 2010. — ISBN-10: 3642127983; ISBN-13: 978-3642127984. Nonlinear Dynamics represents a wide interdisciplinary area of research dealing with a variety of unusual physical phenomena by means of nonlinear differential equations, discrete mappings, and related mathematical algorithms. However, with no real substitute for the linear superposition principle, the methods of...
  • №278
  • 17,09 МБ
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Springer International Publishing AG, 2017. — 228 p. — (Lecture Notes in Mathematics 2193) — ISBN 978-3-319-65183-5. Provides a survey of current research and new approaches in the theory of shadowing of approximate trajectories of dynamical systems see more benefits Focusing on the theory of shadowing of approximate trajectories (pseudotrajectories) of dynamical systems, this...
  • №279
  • 2,40 МБ
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Springer, 2019. — 136 p. This book presents a new approach for the analysis of chaotic behavior in non-linear dynamical systems, in which output can be represented in quaternion parametrization. It offers a new family of methods for the analysis of chaos in the quaternion domain along with extensive numerical experiments performed on human motion data and artificial data. All...
  • №280
  • 5,71 МБ
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Springer Series in Synergetics. Springer-Verlag, Berlin-Heidelberg, 2006, 369 p. Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems. It is encountered in a great variety of settings, both in nature and technology, and has numerous applications ranging from nonlinear...
  • №281
  • 5,67 МБ
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Plakhov A. Springer New York Heidelberg Dordrecht London. 2012. — 284 pages. Notation and Synopsis of Main Results Problem of Minimum Resistance to Translational Motion of Bodies Newton’s Problem in Media with Positive Temperature Scattering in Billiards Problems of Optimal Mass Transportation Problems on Optimization of Mean Resistance The Magnus Effect and the Dynamics...
  • №282
  • 3,53 МБ
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Cambridge: Cambridge University Press, 1993. - 171 p. Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. Emphasis is placed on generality and on the crucial role of measure theory, although no...
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  • 4,93 МБ
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Birkhäuser Basel, 2014. — 310 p. The exposition in the book begins with the consideration of the key elements lying at the foundation of Lobachevsky’s geometry, including its interpretations (models), and is carried out in a form adapted to the methods of modern geometry, function theory, and the theory of nonlinear differential equations. The central part of the book is devoted...
  • №284
  • 5,97 МБ
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North-Holand, 2000 - 107 стр. Introduction. Quantization of the 3D Sinai billiard. Quantal spectral statistics. Classical periodic orbits. Semiclassical analysis. The accuracy of the semiclassical energy spectrum. Semiclassical theory of spectral statistics. Summary.
  • №285
  • 1,75 МБ
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Spain, Springer, 1997 - 202 стр. Saddle-Focus Connections. The Unimodal Family. Contractive Directions. Critical Points of the Bidimensional Map. The Inductive Process. The Binding Point. The Binding Period. The Exclusion of Parameters.
  • №286
  • 1,15 МБ
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Beijing: Springer, Kluwer Academic Publishers, 2001. -402p Nonlinear Control Systems and Power System Dynamics presents a comprehensive description of nonlinear control of electric power systems using nonlinear control theory, which is developed by the differential geometric approach and nonlinear robust control method. This book explains in detail the concepts, theorems and...
  • №287
  • 13,60 МБ
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New York: Wiley-VCH, 2004. - 606p. This reference work provides a comprehensive insight into past developments in the application of non–linear dynamics, such as production systems in the manufacturing and process engineering, mechanical engineering and plant construction and automation technology.
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  • 20,53 МБ
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Springer, 1991. - 178 Pages. Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and technical applications needs to be improved. The bifurcation behavior of periodic solutions...
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Cambridge: Cambridge University Press, 2011. — 219 p. This accessible research monograph investigates how 'finite-dimensional' sets can be embedded into finite-dimensional Euclidean spaces. The first part brings together a number of abstract embedding results, and provides a unified treatment of four definitions of dimension that arise in disparate fields: Lebesgue covering...
  • №290
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Singapore: World Scientific, 2017. — 194 p. The Geometric Theory of Foliations is one of the fields in Mathematics that gathers several distinct domains: Topology, Dynamical Systems, Differential Topology and Geometry, among others. Its great development has allowed a better comprehension of several phenomena of mathematical and physical nature. Our book contains material dating...
  • №291
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Academic Press, 1989. - 187 Pages. The study of differentiate dynamical systems — differentiate dynamics — has been one of the most successful fields of mathematical research in the last twenty years. Many profound results have been uncovered and applied to other branches of mathematics as well as to the natural sciences. The explosive development of the subject has...
  • №292
  • 1,43 МБ
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Chapman and Hall, 2000. — 315 p. Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents a myriad of...
  • №293
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Springer, 1986. — 269 p. Proceedings of a Workshop Held at the Naval Surface Weapons Center, Silver Spring, MD, July 23–26, 1984. Contents: Global aspects of periodic solutions of nonlinear conservative system M. S. Berger Lecture 1: On resonant hamiltonian systems with finitely many degrees of freedom. Martin Kummer Lecture 2: Realizations of the reduced phase space of a...
  • №294
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Berlin: VDM Verlag Dr. Müller, 2010. - 654p. Differential and difference equations have long played important roles in the history of theoretical models. The oscillation theory as a part of the qualitative theory of these types of equations has been developed rapidly in the past thirty years. The extensive application prospect facilitates the development of this field. Our...
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Saarbrucken: Lambert Academic Publishing, 2010. — 587 p. The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger is an area of mathematics and has been created in order to unify the study of differential and difference equations. The oscillation theory as a part of the qualitative theory of dynamic equations on time scales has been developed...
  • №296
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Boston: Kluwer Academic Publishers, 2004. — 318 p. Introduction Averaging Method in Oscillation Systems with Variable Frequencies Aceraging Method in Multipoint Problems Integral Manifolds Investigation of a Dynamical System in a Neighborhood of a Quasiperiodic Trajectory back-matter
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Springer, 1999. - 704 pages. There has been a great deal of excitement over the last few years concerning the emergence of new mathematical techniques for the analysis and control of nonlinear systems: witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos and other complicated dynamical behaviour and the development of a comprehensive theory...
  • №298
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2000. — 289 p. — ISBN 0-13-185000-8. This is the internet version of Invitation to Dynamical Systems. Unfortunately, the original publisher has let this book go out of print. The version you are now reading is pretty close to the original version (some formatting has changed, so page numbers are unlikely to be the same, and the fonts are different). Popular treatments of chaos,...
  • №299
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World Scientific, 2007. - 453 p. - Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research, and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behavior has entered statistical physics, physical chemistry, biophysics,...
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A K Peters, 2009. — 600 p. Complex Dynamics: Families and Friends features contributions by many of the leading mathematicians in the field, such as Mikhail Lyubich, John Milnor, Mitsuhiro Shishikura, and William Thurston. Some of the chapters, including an introduction by Thurston to the general subject of complex dynamics, are classic manuscripts that were never published...
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Cambridge: Cambridge University Press, 2016. — 230 p. Multi-scale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines. Several methodologies exist to retrieve this multi-scale information from a given time series; however, each method has its own limitations. This book presents the...
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N.-Y.: Wiley-VCH, 2007. - 852p. This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions...
  • №303
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Wiley, 2008. - 229 p. Adopting a cross–disciplinary approach, the review character of this monograph sets it apart from specialized journals. The editor is advised by a first–class board of international scientists, such that the carefully selected and invited contributions represent the latest and most relevant findings. The resulting review enables both researchers and...
  • №304
  • 2,87 МБ
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Wiley, 2010. - 262 p. Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new...
  • №305
  • 4,24 МБ
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Wiley-VCH, 2009. - 258 pages. Adopting a cross–disciplinary approach, the review character of this monograph sets it apart from specialized journals. The editor is advised by a first–class board of international scientists, such that the carefully selected and invited contributions represent the latest and most relevant findings. The resulting review uses a common language and...
  • №306
  • 4,59 МБ
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Princeton: Princeton University Press, 2009. — 321 p. Outer billiards is a basic dynamical system defined relative to a convex shape in the plane. B. H. Neumann introduced this system in the 1950s, and J. Moser popularized it as a toy model for celestial mechanics. All along, the so-called Moser-Neumann question has been one of the central problems in the field. This question asks...
  • №307
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Berlin: Springer-Verlag. - 2007. - 370 p. (The Frontiers collection) It has been suggested that the big questions of science are answered – that science has entered a "twilight age" where all the important knowledge is known and only the details need mopping up. And yet, the unprecedented progress in science and technology in the twentieth century has raised questions that weren't...
  • №308
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London: Springer, 2011. - 284p. Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using Lyapunov functionals. Lyapunov Functionals and...
  • №309
  • 4,28 МБ
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New York: Springer, 2017. — 136 p. This thesis develops several systematic and unified approaches for analyzing dynamic systems with positive characteristics or a more general cone invariance property. Based on these analysis results, it uses linear programming tools to address static output feedback synthesis problems with a focus on optimal gain performances. Owing to their low...
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  • 1,84 МБ
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Singapore: World Scientific Publishing Company, 2014. — 258 p. This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering,...
  • №311
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Springer. Second, Expanded and Revised Edition. General Ergodic Theory of Groups of Measure Preserving Transformations, Ergodic Theory of Smooth Dynamical Systems, Dynamical Systems on Homogeneous Spaces, The Dynamics of Billiard Flows in Rational Polygons, Dynamical Systems of Statistical Mechanics and Kinetic Equations.
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CRC Press, 2015. - 304 pp. Excitable media comprise a class of models for a wide range of physical, chemical, and biological systems that exhibit spontaneous formation of spatial patterns. Patterns in Excitable Media: Genesis, Dynamics, and Control explores several aspects of the dynamics of such patterns—in particular their evolution upon interaction with structural and...
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L.: Anthem Press, 2006. - 323p. An attempt to familiarize the reader with nonlinear systems, in particular qualitative characteristics in a variety of systems amenable to mathematization. Contents : Preamble Motivation Recapturing linear ordinary differential equations Linear systems : qualitative behaviour Stability studies Study of equilibria : another...
  • №314
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Springer-Verlag Berlin Heidelberg, 2008. — 383 p. — (Lecture Notes in Physics 730). — ISBN: 978-3-540-72997-6 (eBook), 978-3-642-09210-7 (Softcover), 978-3-540-72996-9 (Hardcover). For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview...
  • №315
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Singapore: World Scientific Publishing, 1993. — 180 p. — ISBN 981-02-1355-7 Простое введение в теорию точечных преобразований, с приложениями к проблеме интегрируемости нелинейных дифференциальных и разностных уравнений. First-order ordinary differential equation Second-order ordinary differential equations Second-order ordinary differential equation Systems of second-order...
  • №316
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Singapore, World Scientific Publishing, 2005. - 607 p. Книга посвящена вопросам нелинейной и хаотической динамики, включая фракталы, вейвлеты, клеточные автоматы, нейросети, скрытые марковские процессы, нечёткую логику и т.п.
  • №317
  • 22,12 МБ
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World Scientific Publishing Company, 1999. - 585 pages. This book is an overview of all of the components of nonlinear dynamics. Nonlinear dynamics is a field of study that enables well-constructed predictive modeling of systems that might be difficult to solve otherwise. Such continuous systems were first widely modeled by ordinary and differential equations, but with the...
  • №318
  • 14,75 МБ
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World Scientific, 2001. — 596 p. The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++, SymbolicC++...
  • №319
  • 2,41 МБ
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Singapore: World Scientific, 2005. - 607p. The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++,...
  • №320
  • 2,71 МБ
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Singapore: World Scientific Publishing Company, 2009. - 225p. This book is devoted to the phenomenon of synchronization and its application for determining the values of Lyapunov exponents. In recent years, the idea of synchronization has become an object of great interest in many areas of science, e.g., biology, communication or laser physics. Over the last decade, new types...
  • №321
  • 20,61 МБ
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New York: Westview Press, 2001. - 505p. An introductory text in nonlinear dynamics and chaos, emphasizing applications in several areas of science, which include vibrations, biological rhythms, insect outbreaks, and genetic control systems. Contains a rich selection of illustrations, with many exercises and examples.
  • №322
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Perseus Books Publishing, 2000. — 516 p. — ISBN 0-7382-0453-6. This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their...
  • №323
  • 6,02 МБ
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New York: Springer, 1996. — 221 p. In 1992 two successive symposia were held in Japan on algorithms, fractals and dynamical systems. The first one was Hayashibara Forum '92: International Symposium on New Bases for Engineering Science, Algorithms, Dynamics and Fractals held at Fujisaki Institute of Hayashibara Biochemical Laboratories, Inc. in Okayama during November 23-28 in...
  • №324
  • 6,48 МБ
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Cambridge University Press, 2014. - 511 pp. Introducing a unified framework for describing and understanding complex interacting systems common in physics, chemistry, biology, ecology, and the social sciences, this comprehensive overview of dynamic critical phenomena covers the description of systems at thermal equilibrium, quantum systems, and non-equilibrium systems. This book...
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Springer, 2010. - 434 pages. This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include: Chaotic Dynamics and Transport in...
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Springer International Publishing AG, 2017. — 184 p. — (Springer Theses) — ISBN: 9783319-529493 Fractional-order calculus offers a novelmodeling approach for systems with extraordinary dynamical properties by introducing the notion of a derivative of noninteger (fractional) order. During the last 300 years fractional-order calculus has been the subject of moderately active...
  • №327
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Springer Cham Heidelberg New York Dordrecht London, 2014. VIII, 368 p. 162 illus. — (Computational Methods in Applied Sciences, Vol. 35). Contributions by the most distinguished researchers in the field Coverage of the most relevant scientific topics in the field High-level scientific quality By having its origin in analytical and continuum mechanics, as well as in...
  • №328
  • 13,50 МБ
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N.-Y.: Springer, 2015. -361p. This book presents recent advances, new ideas and novel techniques related to the field of nonlinear dynamics, including localized pattern formation, self-organization and chaos. Various natural systems ranging from nonlinear optics to mechanics, fluids and magnetic are considered. The aim of this book is to gather specialists from these various...
  • №329
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Springer, 2016. - 298 pp. The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with...
  • №330
  • 7,19 МБ
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Springer-Verlag Berlin, 2010, 298 pages Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The...
  • №331
  • 2,78 МБ
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Nova Science Publishers, Inc., 2017. — 576 p. — (Theoretical and Applied Mathematics). — ISBN 10 1536120324, 13 978-1536120325. The book has two volumes and consists of forty-four chapters, which are divided into five sections: Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; theoretical and...
  • №332
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Nova Science Publishers, Inc., 2017. — 374 p. — (Theoretical and Applied Mathematics). — ISBN 10 1536121630, 13 978-1536121636. The book has two volumes and consists of forty-four chapters, which are divided into five sections: Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; theoretical and...
  • №333
  • 11,33 МБ
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Springer International Publishing AG, 2017. — 145 p. — (Springer Series in Synergetics) — ISBN: 978-3-319-51892-3 This book is primarily concerned with the computational aspects of predictability of dynamical systems – in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for...
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Springer International Publishing, 2017. — 234 p. — (Lecture Notes in Control and Information Sciences 470). — ISBN: 978-3-319-30357-4;, 978-3-319-30356-7. This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that...
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Cambridge: Cambridge University Press, 2014. - 213p. The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the...
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Cambridge: Cambridge University Press, 2016. — 556 p. Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples...
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2nd Edition. — American Mathematical Society, 1999. — 315 p. — ISBN 0821809423. The publication of this book in 1970 marked the culmination of a particularly exciting period in the history of the topology of manifolds. The world of high-dimensional manifolds had been opened up to the classification methods of algebraic topology by Thom's work in 1952 on transversality and...
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Philadelphia: American Mathematical Society, 2016. — 205 p. This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the...
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Springer International Publishing, 2014. — 206 p. — (Graduate Texts in Physics). — ISBN: 978-3-319-06343-0, 978-3-319-06342-3. The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos,...
  • №340
  • 5,52 МБ
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Springer International Publishing Switzerland, 2016. – 329 p. – ISBN-10: 3319263676. This book mostly results from a selection of papers presented during the 11th IFAC (International Federation of Automatic Control) Workshop on Time-Delay Systems, which took place in Grenoble, France, February 4 - 6, 2013. During this event, 37 papers were presented. Taking into account the...
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Elsevier, 2005. — 321 p. Preface Molecular vibration Concepts of dynamical groups Concepts of nonlinear dynamics Application of su(2) algebra Application of noncompact su(1,1) algebra Breaking of su(3) algebra and its application Application of su(3) algebra Quantal effect of asymmetric molecular rotation Pendulum, resonance and molecular highly excited vibration Quasiperiodicity,...
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  • 22,05 МБ
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Springer International Publishing AG, 2017. — 257 p. — ISBN 3319582852. This monograph summarizes the recent major achievements in Möbius invariant Qk spaces. First introduced by Hasi Wulan and his collaborators, the theory of Qk spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers...
  • №343
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Springer, 2010. - 218 p. - This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the...
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Springer, 1997. — 555 p. This book deals with predictability and dynamical concepts in biology and physics. The main emphasis is on intrinsic stochasticity caused by the instability of dynamical equations. In particular, the authors present for the first time in book form their concept of terminal dynamics. They demonstrate that instability as an attribute of dynamical models can...
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Springer, 2018. — 135 p. — (Lecture Notes in Mathematics 2214). — ISBN 3319788094. This monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and...
  • №346
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European Mathematical Society, 2010. - 363 pages. This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit...
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  • 4,20 МБ
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Springer, 2014. - 292 p. - This book is based on the outcome of the 2012 Interdisciplinary Symposium on Complex Systems held at the island of Kos. The book consists of 12 selected papers of the symposium starting with a comprehensive overview and classification of complexity problems, continuing by chapters about complexity, its observation, modeling and its applications to...
  • №348
  • 8,31 МБ
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World Scientific Publishing Company, 2011. - 268 pages. This collection of review articles is devoted to new developments in the study of chaotic dynamical systems with some open problems and challenges. The papers, written by many of the leading experts in the field, cover both the experimental and theoretical aspects of the subject. This edited volume presents a variety of...
  • №349
  • 3,56 МБ
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New York: Springer, 2017. — 240 p. Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and...
  • №350
  • 2,19 МБ
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Springer, 2018. — 265 p. Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: constructive existence results and regularity theorems for all weak solutions; convergence results for solutions and their...
  • №351
  • 5,90 МБ
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Singapore: Springer, 2017. — 278 p. This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research...
  • №352
  • 3,57 МБ
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Springer, 2011. — 538 p. — ISBN 978-94-007-0731-3. Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics....
  • №353
  • 7,03 МБ
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Учебное пособие. – Самара: Изд-во Самар. гос. аэрокосм. ун-та, 2010. – 93 с. Пособие посвящено описанию методов исследования нелинейных колебаний механических систем. В пособии представлены как классические результаты теории нелинейных колебаний, так и асимптотические методы нелинейной механики. Рассмотрены примеры применения методов теории нелинейных колебаний к исследованию...
  • №354
  • 1,95 МБ
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М.: Изд-во МГУ, 2000. — 173 с. Книга написана на основе лекций, читаемых авторами в течение ряда лет для студентов старших курсов физического факультета МГУ. Курс лекций ставит своей целью ознакомить студентов с относительно новым разделом математической физики — теорией особенностей отображений множеств, называемой также иногда теорией катастроф, и ее приложениями в физике....
  • №355
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91 стр., 2009 г. 5 курс, прикладная математика и информатика (кафедра математической кибернетики и компьютерных наук), Саратовский государственный университет. Предметной областью данного пособия являются математические основы построения, анализа и синтеза комбинированных динамических систем. Расчет и проектирование современных технических систем требует построения и...
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Саратов, Берлин, Сент- Луис, сентябрь, 2011 г. — 535 стр. Настоящая книга представляет собой фундаментальный труд по основам нелинейной динамики хаотических и стохастических систем. Книга включает исчерпывающее введение в теорию динамических и стохастических систем и детальный анализ современных результатов, в основном полученных авторами. Каждая из глав книги построена таким...
  • №357
  • 19,54 МБ
  • дата добавления неизвестна
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Саратов, Берлин, Сент-Луис, 2004. - 535 с. Издательство не указано. Настоящая книга представляет собой фундаментальный труд по основам нелинейной динамики хаотических и стохастических систем. Книга включает исчерпывающее введение в теорию динамических и стохастических систем и детальный анализ современных результатов, в основном полученных авторами. Каждая из глав книги построена...
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Институт компьютерных исследований. Год издания: 2002. Количество страниц: 143. В книге представлены 10 лекций по теоретическим основам нелинейной динамики систем с конечным числом степеней свободы (в третье издание лекций, по сравнению с первым, добавлены 3 лекции). Для обсуждения в книге выбраны ряд ключевых проблем, которые относятся к фундаментальным основам нелинейной...
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М.: Наука, 1990. –312 с. Книга подробно рассматривает предмет компьютерного моделирования. Подходит для научных работников, инженеров-исследователей, аспирантов и студентов. Вот некоторые из глав книги: Динамическая система и ее мат. модель Классификация динамических систем Дифференциальные уравнения Колебательные системы. Свойства Фазовые портреты типовых...
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М: Наука, 1990. — 312 с. Методами численного и физического экспериментов исследуются общие закономерности развития и свойства хаотических колебаний на примере радиофизических систем. Анализируются типичные бифуркации регулярных к странных аттракторов, вызываемые изменением параметров и воздействием флуктуаций. Обосновывается методика экспериментальных исследований динамического...
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Москва; Ижевск: Научно-издательский центр «Регулярная и хаотическая динамика», 2008. - 144 с. Книга посвящена систематическому изложению результатов теоретического, численного и экпериментального анализа эффектов синхронизации периодических, квазипериодических, хаотических и стохастичеческих колебаний. Подробно излагается классическая теория синхронизации и обсуждаются пределы...
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Долгопрудный: Интеллект, 2009. — 312 с. — ISBN 978-5-91559-066-2. В книге наиболее полно и последовательно излагается классическая теория периодических автоколебании, внешней и взаимной синхронизации и влияния флуктуаций на свойства периодических автоколебаний. Результаты используются для анализа проблемы генерирования и синхронизации более сложных (квазипериодических и...
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Москва, Ижевск: НИЦ "Регулярная и хаотическая динамика". 2011. — 516 c. — ISBN: 978-5-93972-920-8 Качество: Хороший скан В лекционном курсе по фундаментальным аспектам нелинейной динамики детерминированных и стохастических систем излагаются основы теории динамических систем, теории устойчивости и бифуркаций, теории фракталов и размерности; анализируются основные нелинейные...
  • №364
  • 9,03 МБ
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М.: Наука, 1989. — 96 с. В книге, написанной на основе лекции для студен­тов, посвя­щённой трёхсот­летию «Мате­мати­ческих начал нату­раль­ной фило­софии» Нью­тона, расска­зыва­ется о рож­дении совре­мен­ной мате­ма­тики и тео­рети­ческой физики в трудах вели­ких учёных XVII века. Неко­торые идеи Гюй­генса и Нью­тона опере­дили своё время на несколь­ко столе­тий и полу­чили...
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  • 1,09 МБ
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М.: ВИНИТИ, 1986. - 284 с. Итоги науки и техники. Серия "Современные проблемы математики. Фундаментальные направления". Том 5, Научный редактор член-корреспондент АН СССР Р. В. Гамкрелидзе. Серия издается с 1985 г. Обзор посвящен теории бифуркаций в динамических системах. Наряду с известными, обзор включает ряд новых результа-результатов; некоторые из них известны авторам из...
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  • 3,89 МБ
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3-е изд., доп. — М.: Наука, 1990. — 128 с. Математическое описание катастроф - скачкообразных изменений, возникающих в виде внезапного ответа на плавное изменение внешних условий, дается теориями особенностей и бифуркаций. Их применения к конкретным задачам науки вызвали много споров. В книге рассказывается о том, что же такое теория катастроф и почему она вызывает такие...
  • №367
  • 7,57 МБ
  • дата добавления неизвестна
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3-е изд., доп. — М.: Наука, 1990. — 128 с. Математическое описание катастроф - скачкообразных изменений, возникающих в виде внезапного ответа на плавное изменение внешних условий, дается теориями особенностей и бифуркаций. Их применения к конкретным задачам науки вызвали много споров. В книге рассказывается о том, что же такое теория катастроф и почему она вызывает такие споры....
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