A four-dimensional chaotic system with coexisting attractors and its backstepping control and synchronization

• Published in: Integration (Amsterdam) Vol. 91; pp. 67 - 78
• Main Authors: Yan, Shaohui, Wang, Jianjian, Wang, Ertong, Wang, Qiyu, Sun, Xi, Li, Lin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2023
• Subjects: Backstepping synchronization; Circuit implementation; coexisting Attractors; Offset boosting; SE; Backstepping synchronization; Circuit implementation; Offset boosting; coexisting Attractors
• ISSN: 0167-9260; 1872-7522
• DOI: 10.1016/j.vlsi.2023.03.001

This paper constructs a new four-dimensional dissipative chaotic system with coexisting attractors. The system's dynamic behaviors are analyzed through the numerical simulation of the phase portrait, Lyapunov exponent graph, bifurcation diagram, etc. Numerical simulation results indicate that the system has abundant dynamic characteristics, and the polarity of the chaotic signal can be flexibly changed by introducing offset boosting control. By studying the spectral entropy (SE) complexity of the two different initial conditions, an initial condition with higher complexity is selected as the initial state when the system is synchronized. Finally, a backstepping controller is designed to implement the synchronization of the chaotic system. Multisim is used to simulate the system's circuit and field programmable gate arrays (FPGA) are used to implement the system on actual hardware. •Design of a four-dimensional chaotic system based on coexisting and its synchronous control.•Introduce the control variable m to realize the offset-boosting control of a system.•The backstepping control method is a recursive design process.•Backstepping synchronization avoids the pain and complexity of designing multiple controllers.