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Constructing conditional symmetry in symmetric chaotic systems

Author

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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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    1. Bao, B.C. & Bao, H. & Wang, N. & Chen, M. & Xu, Q., 2017. "Hidden extreme multistability in memristive hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 102-111.
    2. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Kengne, Jacques & Jafari, Sajad & Pham, Viet-Thanh, 2018. "A new four-dimensional system containing chaotic or hyper-chaotic attractors with no equilibrium, a line of equilibria and unstable equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 108-118.
    3. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    4. Zhenyu Gu & Chunbiao Li & Herbert H. C. Iu & Fuhong Min & Yibo Zhao, 2019. "Constructing hyperchaotic attractors of conditional symmetry," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(10), pages 1-9, October.
    5. Sprott, J.C. & Munmuangsaen, Buncha, 2018. "Comment on “A hidden chaotic attractor in the classical Lorenz system”," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 261-262.
    6. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
    7. Munmuangsaen, Buncha & Srisuchinwong, Banlue, 2018. "A hidden chaotic attractor in the classical Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 61-66.
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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).
    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).

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