Recent Improvements in the Theory of Chaotic Attractors

Auteur

René 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.

Michal Pluháek is Associate Professor at Tomas Bata University in Zlin. His research focus includes theory and applications of evolutionary computation, swarm intelligence, swarm robotics, and artificial intelligence in general.

Texte du rabat

This book presents some exceptional developments in chaotic attractor theory encompassing several new directions of research such as three-dimensional axiom A-diffeomorphisms, Shilnikov attractors, dendrites and finite graphs. The chapters in this book were originally published in Journal of Difference Equations and Applications.

Contenu

Introduction: Recent Improvements in the Theory of Chaotic Attractors 1. On the quasi-hyperbolic regime in a certain family of 2-D piecewise linear maps 2. Right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis 3. Search for invariant sets of the generalized tent map 4. On Shilnikov attractors of three-dimensional flows and maps 5. Chaotic attractors of discrete dynamical systems used in the core of evolutionary algorithms: state of art and perspectives 6. Chaos in popular metaheuristic optimizers a bibliographic analysis 7. Ramified continua as global attractors of C1-smooth self-maps of a cylinder close to skew products 8. Dynamics of three-dimensional A-diffeomorphisms with two-dimensional attractors and repellers 9. Chaotic behaviour of countable products of homeomorphism groups 10. Remarks on minimal sets on dendrites and finite graphs 11. Recurrence and nonwandering sets of local dendrite maps 12. Diffeomorphisms with infinitely many Smale horseshoes