This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA.
This book offers a captivating exploration of the intersection between mathematics, chaos theory, and dynamical systems through the personal journeys of twelve renowned mathematicians and physicists from China, Europe, Russia, and the USA.
The first section of the book provides an intimate look into the formative experiences and early steps of these scientists. In these life stories, the names of other famous mathematicians arise, crisscrossing all the stories in unexpected ways. The second part of the book explores the practical applications of chaotic attractors in various fields. These include chaos-based encryption in cryptography, sensor and actuator placement in Chua circuits for control systems, and chaotic dynamics in remote sensing for crop modeling. It also highlights the role of chaos theory in the development of memristors following Leon Chua’s 1971 discovery, leading to advances in nonlinear dynamics, hyperchaos, and memristor-based systems. The chapters further examine how chaos theory addresses modern challenges such as modeling COVID-19 spread using SEIR models and optimizing mobile network design, demonstrating the wide-reaching impact of chaotic systems in real-world applications.
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.
This book includes a revised introduction and a new chapter. The remaining chapters were originally published in Journal of Difference Equations and Applications.
Introduction: Dynamical systems: Paths of Twelve Mathematicians and
Physicists toward the Chaos and its applications
1. The paths of nine
mathematicians to the realm of dynamical systems
2. Two more mathematicians
and one physicist tell what motivated their careers and how they began
3.
Optimal placement of sensor and actuator for controlling the piecewise linear
Chua circuit via a discretized controller
4. Nonlinear dynamics and
hyperchaos in a modified memristor-based Chua's circuit and its generalized
discrete system
5. Memristor-based Gauss chaotic maps with hidden/self-exited
dynamics
6. Enhanced design and hardware implementation of a chaos-based
block cipher for image protection
7. On secure communication scheme-based
mixed discrete-time hyperchaotic systems
8. On the use of chaotic dynamics
for mobile network design and analysis: towards a trace data generator
9. The
SEIR Covid-19 model described by fractional-order difference equations:
analysis and application with real data in Brazil
10. Chaotic attractors
captured from remote sensing time series for the dynamics of cereal crops
11.
Nonlinear dynamic and chaos in a remanufacturing duopoly game with
heterogeneous players and nonlinear inverse demand functions
René Lozi is Emeritus Professor at University Cote dAzur, 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.
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.
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.
