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, Henon and Belykh attractors. Existence proofs for strange attractors in piecewise-smooth nonlinear Lozi-Henon 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 Henon 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.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Postgraduate, Undergraduate Advanced, and Undergraduate Core
Maße
Höhe: 250 mm
Breite: 175 mm
Dicke: 19 mm
Gewicht
ISBN-13
978-1-032-94042-7 (9781032940427)
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Schweitzer Klassifikation
Rene Lozi is Emeritus Professor at University Cote d'Azur, France and Vice-President of the International Society of Difference Equations. His research areas include complexity and emergence theory, dynamical systems, bifurcations, control of chaos, cryptography based on chaos, and memristors
Lyudmila Efremova is Professor at Nizhny Novgorod State University and Moscow Institute of Physics and Technology, Russia. Her scientific interests include regular and chaotic properties of low-dimensional discrete dynamical systems.
Mohammed-Salah Abdelouahab is Professor at Abdelhafid Boussouf University Center of Mila, Algeria. He is the head of the research team in fractional calculus and its applications at the laboratory of mathematics and their interactions and the Editor-in-Chief of the Journal of Innovative Applied Mathematics and Computational Sciences.
Safwan El Assad is Professor at Polytech Nantes, France. Between 1988 to 2005, his research activities concerned radar imagery and digital communications. Nowadays his research largely focuses on chaos-based cryptography, encryption, crypto-compression, steganography, hash functions, authenticated encryption.
Introduction - Lozi, Henon, and Belykh chaotic attractors: new results fifty years on 1. Controlling chaotic transients in the Henon and the Lozi map with the safety function 2. On target-oriented control of Henon and Lozi maps 3. Controlling chimera and solitary states by additive noise in networks of chaotic maps 4. Statistical self-similarity in Lozi and Henon'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-Henon 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
