Recent Improvements In The Theory Of Chaotic Attractors

Recent Improvements in the Theory of Chaotic Attractors

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) and symbolized by the “butterfly effect”. Relevant new results have been collected in this book, including: Some remarks on minimal sets on dendrites and finite graphs and the study of recurrence and nonwandering sets of local dendrite maps. Ramified continua as global attractors of C1- smooth self-maps of a cylinder close to skew products Chaotic behaviour of countable products of homeomorphism groups and dynamics of three-dimensional axiom A-diffeomorphisms with two-dimensional attractors and repellers. The search for invariant sets of the generalized tent map and quasi-hyperbolic regime in a certain family of 2-D piecewise linear map. Shilnikov attractors of three-dimensional flows and maps, right fractional calculus to inverse-time chaotic maps and asymptotic stability analysis and diffeomorphisms with infinitely many Smale horseshoes. The theory of chaotic attractor is also used as a core for evolutionary algorithms and metaheuristic optimizers in this volume. This book will be of great value to 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.

Recent Trends In Chaotic, Nonlinear And Complex Dynamics

Recent Advances in Chaotic Systems and Synchronization

Recent Advances in Chaotic Systems and Synchronization: From Theory to Real World Applications is a major reference for scientists and engineers interested in applying new computational and mathematical tools for solving complex problems related to modeling, analyzing and synchronizing chaotic systems. Furthermore, it offers an array of new, real-world applications in the field. Written by eminent scientists in the field of control theory and nonlinear systems from 19 countries (Cameroon, China, Ethiopia, France, Greece, India, Italia, Iran, Japan, Mexico, and more), this book covers the latest advances in chaos theory, along with the efficiency of novel synchronization approaches. Readers will find the fundamentals and algorithms related to the analysis and synchronization of chaotic systems, along with key applications, including electronic design, text and image encryption, and robot control and tracking. - Explores and evaluates the latest real-world applications of chaos across various engineering and biomedical engineering fields - Investigates advances in chaos synchronization techniques, including the continuous sliding-mode control approach, hybrid synchronization between chaotic and hyperchaotic systems, and neural network synchronization - Presents recent advances in chaotic systems through an overview of new systems and new proprieties