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Constructing conditional symmetry in symmetric chaotic systems

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  • Li, Chunbiao
  • Sprott, Julien Clinton
  • Zhang, Xin
  • Chai, Lin
  • Liu, Zuohua

Abstract

Based on the analysis of polarity balance and exhaustive computer searching, a series of symmetric chaotic flows is found for hosting conditional symmetry. Symmetric structure shapes the elegant symmetric phase trajectory, and conditional symmetry permits the convenience of embedding an extra set of coexisting symmetric attractors. Bifurcation analysis proves the coexistence of two independent processes of dynamical behavior under conditional symmetry. Circuit simulation confirms the numerical and theoretical analysis.

Suggested Citation

  • Li, Chunbiao & Sprott, Julien Clinton & Zhang, Xin & Chai, Lin & Liu, Zuohua, 2022. "Constructing conditional symmetry in symmetric chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010778
    DOI: 10.1016/j.chaos.2021.111723
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    References listed on IDEAS

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    Cited by:

    1. Wang, Ning & Xu, Dan & Kuznetsov, N.V. & Bao, Han & Chen, Mo & Xu, Quan, 2023. "Experimental observation of hidden Chua’s attractor," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Zhenggang Guo & Junjie Wen & Jun Mou, 2022. "Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
    3. Chen, Yuanlin & Lu, Tianxiu & Wang, Qianxue, 2024. "The chaotic properties and circuit design of a generalized high-dimensional integer-domain system," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    4. Zhoubin Sheng & Chunbiao Li & Yikai Gao & Zhinan Li & Lin Chai, 2023. "A Switchable Chaotic Oscillator with Multiscale Amplitude/Frequency Control," Mathematics, MDPI, vol. 11(3), pages 1-11, January.
    5. Sivaganesh, G. & Srinivasan, K. & Fozin, T. Fonzin & Pradeep, R. Gladwin, 2023. "Emergence of chaotic hysteresis in a second-order non-autonomous chaotic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    7. Zhang, Fangfang & Zhang, Shuaihu & Chen, Guanrong & Li, Chunbiao & Li, Zhengfeng & Pan, Changchun, 2022. "Special attractors and dynamic transport of the hybrid-order complex Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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