This book presents the latest international research achievements in complex chaotic systems, establishing itself as an reference with high value in nonlinear dynamics and chaos theory. The book systematically explores dynamical behaviors of complex chaotic systems through control methods and engineering technologies, with particular emphasis on chaos synchronization and its revolutionary applications in secure communication. It introduces chaos synchronization including anti-synchronization, projective synchronization, hybrid projective synchronization, and various advanced synchronization techniques for both integer-order and fractional-order complex chaotic systems. Furthermore, the work demonstrates pioneering applications of chaotic systems and synchronization technologies in the field of secure communication. This publication stands out through its comprehensive pedagogical features, which include detailed mathematical frameworks and illustrative case studies. The content is strategically organized to guide readers progressively from fundamental concepts in Chapter 1, through various synchronization types of integer-order systems in Chapters 2-12, followed by in-depth analysis of fractional-order systems in Chapters 13-18, and culminating with practical encryption applications in the final chapters. The principal merit of this work resides in its distinctive integration of theoretical rigor and practical applicability, providing readers with both foundational comprehension and executable methodologies for complex system analysis. It serves not only as an essential reference resource for secure communication but also establishes a solid theoretical foundation and offers innovative methodological pathways for researchers exploring complex systems.
Table of Contents:
Introduction and Preliminary Knowledge.- Anti-synchronization of complex chaotic systems.
About the Author :
Shutang Liu, Ph.D., is a Second-Level Professor and Doctoral Supervisor at Shandong University, a recipient of the Top 100 National Excellent Doctoral Dissertations Award, and a former visiting scholar at The University of Manchester. His research focuses on nonlinear theory, control and application analysis in nonlinear dynamical systems, fractal and chaos theory and control, astrophysics, physical oceanography, and marine ecology. He has published nearly 400 papers in leading and other scholarly journals. As the first author, he has published five monographs with Springer: Fractal Control Theory, Fractal Control and Its Applications, Mathematical Principle and Fractal Analysis of Mesoscale Eddy, Surface Chaos and Its Applications, and Pattern Dynamics of Marine Plankton Behavior. He has also authored a monograph with American Academic Press titled Mathematical Principles of Black Holes and Dark Matter. He has led four National Key Fund Projects and over ten other projects, including General Programs of the National Natural Science Foundation of China. He serves as a member of the Chaos Secure Communication Committee of the Chinese Association for Cryptologic Research, Vice Chairman of the Circuit and System Subcommittee of the Chinese Institute of Electronics, a reviewer for Mathematical Reviews of the American Mathematical Society, and a member of the American Mathematical Society.
Ping Liu, PhD., Professor of Shandong Agricultural University. She received the B.S. degree in automation from Dalian University major in 2006, the Ph.D. degree in Systems Engineering from Shandong university in 2012. Her research focuses on key technologies of agricultural robots and intelligent assisted breeding. Over the past five years, she has presided over 14 research projects, published over 60 SCI papers, obtained over 20 authorized invention patents, registered over 10 software copyrights, assisted in breeding 1 new wheat variety, and won over 10 awards, including the First Prize of Science and Technology of the Shandong Automation Society.
Cuimei Jiang, Ph.D., is an Associate Professor at Qilu University of Technology (Shandong Academy of Sciences). She received the B.S. degree from Shandong Normal University, the M.S. degree from the Ocean University of China, and the Ph.D. degree from Shandong University. Her research interests include nonlinear dynamical systems, chaos theory and control, and the dynamics of complex networks. In recent years, she has published over 30 papers in international journals such as Chaos, Solitons and Fractals, Mathematical Methods in the Applied Sciences, Chaos, and so on. She has also participated in and led several projects funded by the National Natural Science Foundation of China and provincial-level research programs. Also, she won over 5 awards, including the Second Prize of the Shandong Provincial Higher Education Science and Technology Award.
Changan Liu, who earned his Ph.D. in the United States, is an Associate Researcher Fellow in the Department of Systems Biomedicine at the School of Basic Medical Sciences, Shandong University, and is recognized as an Overseas Scientific Talent in Shandong Province. His research focuses on nonlinear dynamical systems, fractal theory and applications, artificial intelligence and big data, computational biology, biomathematics, and biomedical informatics. He has published over 30 international academic papers and co-authored a monograph published by Springer. Additionally, he has participated in and led multiple national and provincial-level natural science foundation projects.
