Cluster Synchronization of Networks of Chaotic Systems: A Comprehensive Review of Theory and Applications

Abstract

Phenomenon of cluster synchronization has captured the curiosity of scientists in the study of nonlinear dynamics over the last few decades. It is a well-known and intriguing aspect of complex systems that has garnered significant attention in research. Many researchers have significantly addressed the synchronization of cluster-based networks with identical and non-identical systems in the literature. This review paper presents a detailed summary of overall developments in the domain of cluster synchronization of chaotic system networks. After introducing the chaotic systems and concept of cluster synchronization initially; the applicability of synchronization in several fields including secure communication, information processing, and the synchronization of complex networks, has been highlighted in the later part of the paper. In general, for meeting out the goal of cluster synchronization, several strategies including standard Lyapunov design- based approach, pinning control, observer-based control, time-delayed feedback control, adaptive synchronization etc. are prominently used in literature. The article briefly discusses these approaches and reviews their advantages and disadvantages along with some possible applications. The overarching goal of this literature review is to provide a comprehensive summary of current research on cluster synchronization in chaotic systems and to point the way toward promising avenues for further investigation. The overarching goal of this literature review is to provide a comprehensive summary of current research on cluster synchronization in chaotic systems and to point the way toward promising avenues for further investigation.

Keywords:

• Chaotic system
• Cluster synchronization
• Complex network
• Lipschitz conditions
• Lyapunov stability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Akshay Kumar Jaiswal

Akshay Kumar Jaiswal received the BE degree from Government Engineering College, Rewa, India in 2020 and the Mtech degree from National Institute of Technology, Hamirpur, India in 2023. Currently he is pursuing PhD from Indian Institute of Technology, Kanpur, India. His field of interest includes control systems, nonlinear system, chaotic system and cluster synchronization of chaotic system. Corresponding author. Email: [email protected]

Bharat Bhushan Sharma

Bharat Bhushan Sharma received his Btech degree in electrical engineering from Regional Engineering College Hamirpur, India, in 1997. Further, he received his Master in engineering degree in electronics and control from BITS Pilani, India, in 1999. He received his PhD degree in electrical engineering from Indian Institute of Technology Delhi, India, in 2010. His research interests mainly include control & synchronization of nonlinear systems, chaotic dynamics, design of nonlinear observers etc. He has published more than 100 papers in various international journals and conferences of repute in these areas. He is Member of IEEE Control System Society, Institution of Engineers (India) and Robotic Society of India. He is presently working as an associate professor with the Department of Electrical Engineering, National Institute of Technology Hamirpur (Himachal Pradesh), India E-mail: [email protected]