1st Edition

Recent Improvements in the Theory of Chaotic Attractors

Edited By René Lozi, Lyudmila Efremova, Michal Pluháček Copyright 2025
256 Pages
by CRC Press

256 Pages
by CRC Press

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 theory of chaotic attractors has experienced exceptional development over the last fifty years since the revelation of chaos in mathematics (invented by James Yorke)... Read more

Introduction: Recent Improvements in the Theory of Chaotic Attractors

René Lozi, Lyudmila Efremova and Michal Pluhacek

 

1. On the quasi-hyperbolic regime in a certain family of 2-D piecewise linear maps

Asma Ladjeroud and Elhadj Zeraoulia

 

2. Right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis

Guo-Cheng Wu, Jia-Li Wei and Maokang Luo

 

3. Search for invariant sets of the generalized tent map

Kimberly Ayers, Dmitriy Dmitrishin, Ami Radunskaya, Alexander Stokolos and Kostyantyn Stokolos

 

4. On Shilnikov attractors of three-dimensional flows and maps

Yu. V. Bakhanova, S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov and E. A. Samylina

 

5. Chaotic attractors of discrete dynamical systems used in the core of evolutionary algorithms: state of art and perspectives

Ivan Zelinka and Roman Senkerik

 

6. Chaos in popular metaheuristic optimizers – a bibliographic analysis

Michal Pluhacek, Anezka Kazikova, Adam Viktorin, Tomas Kadavy and Roman Senkerik

 

7. Ramified continua as global attractors of C1-smooth self-maps of a cylinder close to skew products

L. S. Efremova

 

8. Dynamics of three-dimensional A-diffeomorphisms with two-dimensional attractors and repellers

Marina Barinova, Vyacheslav Grines and Olga Pochinka

 

9. Chaotic behaviour of countable products of homeomorphism groups

N. I. Zhukova and A. G. Korotkov

 

10. Remarks on minimal sets on dendrites and finite graphs

E. N. Makhrova

 

11. Recurrence and nonwandering sets of local dendrite maps

Hafedh Abdelli, Habib Marzougui and Amira Mchaalia

 

12. Diffeomorphisms with infinitely many Smale horseshoes

Xu Zhang and Guanrong Chen

 

Biography

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 Pluháček 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.