Nonlinear Dynamics of Chaotic and Stochastic Systems Tutorial and Modern Developments
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Vadim S. Anishchenko, Vladimir Astakhov, Alexander Neiman, Tatjana Vadivasova, Lutz Schimansky-Geier
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Nonlinear Dynamics of Chaotic and Stochastic Systems Tutorial and Modern Developments
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Springer-Verlag
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9783540381686
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2
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CHF 48.70
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Theoretische Physik
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English
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446
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Wasserzeichen
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PC/MAC/eReader/Tablet
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PDF
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 preparingthiseditionwemadesom clari?cationsinseveralsection andalso 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 widesectionofreaderswhoarealr adyspecialistsorthosewhoarebe inning 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 Thisbookisdevotedtotheclassic lbackgroundandtocontemporaryr sults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsof oiseonvariousregimesofdynamic ystems 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.Thisbo kisanattempttocombinetheappro chof 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.
Preface to the Second Edition
7
Preface to the First Edition
8
Contents
11
1. Tutorial
15
1.1 Dynamical Systems
15
1.2 Fluctuations in Dynamical Systems
51
1.3 Synchronization of Periodic Systems
94
References
116
2. Dynamical Chaos
123
2.1 Routes to Chaos
123
2.2 Statistical Properties of Dynamical Chaos
153
2.3 Synchronization of Chaos
178
2.4 Effects of Synchronization in Extended Self- Sustained Oscillatory Systems
199
2.5 Synchronization in Living Systems
239
2.6 Controlling Chaos
247
2.7 Reconstruction of Dynamical Systems
278
References
306
3. Stochastic Dynamics
321
3.1 Stochastic Resonance
321
3.2 Synchronization of Stochastic Systems
365
3.3 The Beneficial Role of Noise in Excitable Systems
395
3.4 Noise-Induced Transport
413
References
448
Index
458
