Robust Chaos and Its Applications

by Julien Clinton Sprott, Zeraoulia Elhadj

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular.Contents: Poincare Map Technique, Smale Horseshoe, and Symbolic DynamicsRobustness of ChaosStatistical Properties of Chaotic AttractorsStructural StabilityTransversality, Invariant Foliation, and the Shadowing LemmaChaotic Attractors with Hyperbolic StructureRobust Chaos in Hyperbolic SystemsLorenz-Type SystemsRobust Chaos in the Lorenz-Type SystemsNo Robust Chaos in Quasi-AttractorsRobust Chaos in One-Dimensional MapsRobust Chaos in 2-D Piecewise Smooth Maps
Readership: Advanced undergraduate and graduate students, researchers, engineers and instructors interested in chaos and dynamical systems.

473 pages, ebook

First published January 1, 2011