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

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  • Cai, Xinshan
  • Liu, Ling
  • Wang, Yaoyu
  • Liu, Chongxin

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.

Suggested Citation

  • Cai, Xinshan & Liu, Ling & Wang, Yaoyu & Liu, Chongxin, 2021. "A 3D chaotic system with piece-wise lines shape non-hyperbolic equilibria and its predefined-time control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002587
    DOI: 10.1016/j.chaos.2021.110904
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    References listed on IDEAS

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    Cited by:

    1. Yildirim, Melih, 2022. "Optical color image encryption scheme with a novel DNA encoding algorithm based on a chaotic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Leng, Xiangxin & Gu, Shuangquan & Peng, Qiqi & Du, Baoxiang, 2021. "Study on a four-dimensional fractional-order system with dissipative and conservative properties," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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