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Full Description
Over the past fifty years, the development of chaotic dynamical systems theory and its subsequent wide applicability in science and technology has been an extremely important achievement of modern mathematics. Chaotic attractors are not a fleeting curiosity, and their continued study is important for the progress of mathematics.
This book collects several of the new relevant results on the most important of them: the Lozi, Hénon and Belykh attractors. Existence proofs for strange attractors in piecewise-smooth nonlinear Lozi-Hénon and Belykh maps are given. Generalization of Lozi map in higher dimensions, Markov partition or embedding into the 2D border collision normal form of this map are considered. K-symbol fractional order discrete-time and relationship between this map and maxtype difference equations are explored. Statistical self-similarity, control of chaotic transients, and target-oriented control of Hénon and Lozi attractors are presented. Controlling chimera and solitary states by additive noise in networks of chaotic maps, detecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear maps, and studying border collision bifurcations in a piecewise linear duopoly model complete this book.
This book is an essential companion for students and researchers in mathematics, physics, engineering, and related disciplines seeking to deepen their understanding of chaotic dynamical systems and their applications.
The chapters in this book were originally published in Journal of Difference Equations and Applications.
Contents
Introduction - Lozi, Hénon, and Belykh chaotic attractors: new results fifty years on 1. Controlling chaotic transients in the Hénon and the Lozi map with the safety function 2. On target-oriented control of Hénon and Lozi maps 3. Controlling chimera and solitary states by additive noise in networks of chaotic maps 4. Statistical self-similarity in Lozi and Hénon's strange attractors 5. Markov partition in the attractor of Lozi maps 6. Lozi map embedded into the 2D border collision normal form 7. A higher-dimensional generalization of the Lozi map: bifurcations and dynamics 8. Existence proofs for strange attractors in piecewise-smooth nonlinear Lozi-Hénon and Belykh maps 9. On the relationship between Lozi maps and max-type difference equations 10. K-symbol fractional order discrete-time models of Lozi system 11. Border collision bifurcations in a piecewise linear duopoly model 12. Detecting invariant expanding cones for generating word sets to identify chaos in piecewise-linear maps
