Hyperbolic Chaos : A Physicist’s View

"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia. Front Matter....Pages i-xv Front Matter....Pages 1-1 Dynamical Systems and Hyperbolicity....Pages 3-33 Possible Occurrence of Hyperbolic Attractors....Pages 35-56 Front Matter....Pages 57-57 Kicked Mechanical Models and Differential Equations with Periodic Switch....Pages 59-79 Non-Autonomous Systems of Coupled Self-Oscillators....Pages 81-102 Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincaré Maps....Pages 103-117 Parametric Generators of Hyperbolic Chaos....Pages 119-139 Recognizing the Hyperbolicity: Cone Criterion and Other Approaches....Pages 141-170 Front Matter....Pages 171-171 Systems of Four Alternately Excited Non-autonomous Oscillators....Pages 173-200 Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle....Pages 201-217 Systems with Time-delay Feedback....Pages 219-241 Chaos in Co-operative Dynamics of Alternately Synchronized Ensembles of Globally Coupled Self-oscillators....Pages 243-256 Front Matter....Pages 257-257 Electronic Device with Attractor of Smale-Williams Type....Pages 259-263 Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Maps....Pages 265-272 Conclusion....Pages 273-276 Back Matter....Pages 277-320 This book reviews progress on uniformly hyperbolic attractors in dynamical systems from the perspective of physics. The text shows how to find hyperbolic chaotic attractors in physical systems and how to design physical systems that possess hyperbolic chaos.