Hyperbolic chaos : a physicist's view

Part I. Basic Notions and Review -- Dynamical Systems and Hyperbolicity -- Possible Occurrence of Hyperbolic Attractors -- Part II. Low-Dimensional Models -- Kicked Mechanical Models and Differential Equations with Periodic Switch -- Non-Autonomous Systems of Coupled Self-Oscillators -- Autonomous Low-dimensional Systems with Uniformly Hyperbolic Attractors in the Poincaré Maps -- Parametric Generators of Hyperbolic Chaos -- Recognizing the Hyperbolicity: Cone Criterion and Other Approaches -- Part III. Higher-Dimensional Systems and Phenomena -- Systems of Four Alternately Excited Non-autonomous Oscillators -- Autonomous Systems Based on Dynamics Close to Heteroclinic Cycle -- Systems with Time-delay Feedback -- Chaos in Co-operative Dynamics of Alternately Synchronized Ensembles of Globally Coupled Self-oscillators -- Part IV. Experimental Studies -- Electronic Device with Attractor of Smale-Williams Type -- Delay-time Electronic Devices Generating Trains of Oscillations with Phases Governed by Chaotic Maps -- Conclusion "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. 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.