A 3D chaotic system with piece-wise lines shape non-hyperbolic equilibria and its predefined-time control. (May 2021)

• Record Type: Journal Article
• Authors: Cai, Xinshan; Liu, Ling; Wang, Yaoyu; Liu, Chongxin
• Is Part Of: Chaos, solitons and fractals. Volume 146(2021)
• Publication Date: 2021-05
• Subjects: Chaos -- Hidden attractor -- Non-hyperbolic equilibria -- Predefined-time stability -- Complexity analysis; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.110904
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The novel 3D chaotic system has non-hyperbolic equilibria with piece-wise shape, which is special and rarely mentioned before. The proposed system has a heart-shaped attractor on y - x plane, and a reverse bubble is found in the system, which indicates that the system has anti-monotonicity. The dynamics of the system has been verified by real circuit experiment. A predefined-time stability controller is designed for the system. The system can be successfully controlled within different predefined time by adding only one controller. As far as we know, it is the first time that the predefined-time stability theory has been applied to the control of a chaotic system. Abstract: In this paper, a novel 3D chaotic system with an infinite number of equilibria is proposed and its predefined-time control is studied. The system has non-hyperbolic equilibria with piece-wise shape, which is special and rarely mentioned before. Through 0-1 test, Lyapunov exponent, bifurcation diagram and complexity analysis, the system is deeply investigated. A reverse bubble (Feigenbaum remerging tree) is found in the system, which proves the anti-monotonicity. Furthermore, the circuit of the system is designed and the real experiment is carried out to verify its dynamic characteristics. Finally, according to the theory of predefined-time stability, a predefined time controller is designed for the system. By adding only one controller to the system, the objective of stabilizing the system within a predefined time can be achieved successfully, and simulation analysis shows good performance of the controller.