A 3D chaotic system with piece-wise lines shape non-hyperbolic equilibria and its predefined-time control

Xinshan Cai, Ling Liu, Yaoyu Wang and Chongxin Liu

Chaos, Solitons & Fractals, 2021, vol. 146, issue C

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.

Keywords: Chaos; Hidden attractor; Non-hyperbolic equilibria; Predefined-time stability; Complexity analysis (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002587

DOI: 10.1016/j.chaos.2021.110904

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