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Hyperbolic Chaos: A Physicist's View
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This book is devoted to studies aimed at identifying or design of physical systems,
in which chaotic dynamics occurs associated with uniformly hyperbolic attractors,
such as the Plykin attractor or the Smale – Williams solenoid. Basic notions of
the relevant mathematical theory are discussed, as well as approaches proposed
for constructing systems with hyperbolic attractors. In particular, we consider
models driven with periodic pulses; dynamics consisted of periodically repeated stages,
each of which corresponds to specific form of differential equations; design of systems
of alternately excited oscillators transmitting excitation each other; the use of parametric
excitation of oscillations; introduction of the delayed feedback. Examples of maps,
differential equations, as well as simple mechanical and electronic systems are presented
manifesting chaotic dynamics due to the occurrence of the uniformly hyperbolic attractors.
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Contents:Part I. Basic Notions and Review1 Dynamical Systems and Hyperbolicity2 Possible Occurrence of Hyperbolic Attractors Part II. Low-Dimensional Models3 Kicked Mechanical Models and Differential Equations with Periodic Switch4 Non-Autonomous Systems of Coupled Self-Oscillators 5 Autonomous low-dimensional systems with uniformly hyperbolic attractors in the Poincare maps 6 Parametric Generators of Hyperbolic Chaos 7 Recognizing the Hyperbolicity: Cone Criterion and Other Approaches Part III. Higher-Dimensional Systems and Phenomena8 Systems of four alternately excited non-autonomous oscillators9 Autonomous systems based on dynamics close to heteroclinic circle 10 Systems with time-delay feedback 11 Chaos in cooperative dynamics of alternately synchronized ensembles of globally coupled self-oscillators Part IV. Experimental Studies12 Electronic device with attractor of Smale – Williams type13 Delay-time electronic devices generating trains of oscillations with phases governed by chaotic maps Conclusion: Prospects and Research DirectionsAppendicesList of referencesIndex |
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