Stochastic and Chaotic Oscillations
Stochastic and Chaotic Oscillations

Author: Juri I. Neimark

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 510

ISBN-13: 9401125961

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This volume is devoted to stochastic and chaotic oscillations in dissipative systems. Chapter 1 deals with mathematical models of deterministic, discrete and distributed dynamical systems. In Chapter 2, the two basic trends of order and chaos are considered. The next three chapters describe stochasticity transformers, amplifiers and generators, turbulence, and phase portraits of steady-state motions and their bifurcations. Chapter 6 treats the topics of stochastic and chaotic attractors, and this is followed by two chapters dealing with routes to chaos and the quantitative characteristics of stochastic and chaotic motions. Finally, Chapter 9, which comprises more than one-third of the book, presents examples of systems having chaotic and stochastic motions drawn from mechanical, physical, chemical and biological systems. The book concludes with a comprehensive bibliography. For mathematicians, physicists, chemists and biologists interested in stochastic and chaotic oscillations in dynamical systems.

Nonlinear Dynamics of Chaotic and Stochastic Systems
Nonlinear Dynamics of Chaotic and Stochastic Systems

Author: Vadim S. Anishchenko

Publisher: Springer Science & Business Media

Published: 2007-07-20

Total Pages: 463

ISBN-13: 3540381686

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We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

Nonlinear Dynamics of Chaotic and Stochastic Systems
Nonlinear Dynamics of Chaotic and Stochastic Systems

Author: Vadim S. Anishchenko

Publisher: Springer Science & Business Media

Published: 2003-01-22

Total Pages: 396

ISBN-13: 9783540424192

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Contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.

Regular and Chaotic Oscillations
Regular and Chaotic Oscillations

Author: Polina S. Landa

Publisher: Springer Science & Business Media

Published: 2012-11-12

Total Pages: 401

ISBN-13: 3540452524

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This text maps out the modern theory of non-linear oscillations. The material is presented in a non-traditional manner and emphasises the new results of the theory - obtained partially by the author, who is one of the leading experts in the area. Among the topics are: synchronization and chaotization of self-oscillatory systems and the influence of weak random vibration on modification of characteristics and behaviour of the non-linear systems.

Chaos in Systems with Noise
Chaos in Systems with Noise

Author: Tomasz Kapitaniak

Publisher: World Scientific

Published: 1990

Total Pages: 256

ISBN-13: 9789810204105

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As in the first edition, the influence of random noise on the chaotic behavior of dissipative dynamical systems is investigated. Problems are illustrated by mechanical examples. This revised and updated edition contains new sections on the summary of probability theory, homoclinic chaos, Melnikov method, routes to chaos, stabilization of period-doubling, and Hopf bifurcation by noise. Some chapters have been rewritten and new examples have been added.

Regular and Chaotic Dynamics
Regular and Chaotic Dynamics

Author: A.J. Lichtenberg

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 708

ISBN-13: 1475721846

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This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.

Chaotic Transitions in Deterministic and Stochastic Dynamical Systems
Chaotic Transitions in Deterministic and Stochastic Dynamical Systems

Author: Emil Simiu

Publisher: Princeton University Press

Published: 2014-09-08

Total Pages: 244

ISBN-13: 1400832500

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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.