Dynamical Chaos: Models and Experiments : Appearance Routes and Structure of Chaos in Simple Dynamical Systems

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World Scientific, 1995 - Science - 383 pages
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In this book, bifurcational mechanisms of the development, structure and properties of chaotic attractors are investigated by numerical and physical experiments based on the methods of the modern theory of nonlinear oscillations. The typical bifurcations of regular and chaotic attractors which are due to parameter variations are analyzed.Regularities of the transition to chaos via the collapse of quasiperiodic oscillations with two and three frequencies are investigated in detail. The book deals with the problems of chaotic synchronization, interaction of attractors and the phenomenon of stochastic resonance. The problems of fluctuation influence on the bifurcations and properties of chaotic attractors are investigated more closely.All principal problems are investigated by the comparison of theoretical and numerical results and data from physical experiments.
 

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Contents

Contents
1
Numerical Methods
33
Inertial Nonlinearity Oscillator
69
Autonomous Oscillation Regimes
90
Quasiattractor Structure
122
TwoFrequency Oscillation
146
Breakdown of Two
174
Synchronization of Chaos
199
Nonlinear Phenomena
219
Bifurcations of Dynamical System
268
Chaos Structure and Properties
302
colored noise
308
Reconstruction of Dynamical
337
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