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Reconstitution for interpreting hidden dynamics with stable equilibrium point

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  • Chen, Mo
  • Wang, Chao
  • Bao, Han
  • Ren, Xue
  • Bao, Bocheng
  • Xu, Quan

Abstract

Extreme multistability induced by line or plane equilibrium point sets can be successfully reconstituted in the integral domain to achieve mechanism understanding and physical observation. Inspired by this, hidden dynamics with stable equilibrium point, a peculiar multistability, may also be interpreted in the integral domain. To this end, a three-dimensional (3-D) quadratic jerk system with hidden chaotic and periodic behaviors is selected as a representative paradigm to disclose the reconstituted hidden dynamics. Through integral and linear transformations, a 3-D reconstituted system with standalone initials-related constant parameters is constructed. Similar to the original system, the reconstituted system possesses one stable equilibrium point but can reconstitute the previous dynamical behaviors while initiating from the origin point. The immediate benefit is that the reconstituted hidden dynamical behaviors are relatively easier to be observed in a physical circuit. Finally, the physical circuit is designed and circuit simulations are performed by Power SIMulation (PSIM) to validate the numerical results.

Suggested Citation

  • Chen, Mo & Wang, Chao & Bao, Han & Ren, Xue & Bao, Bocheng & Xu, Quan, 2020. "Reconstitution for interpreting hidden dynamics with stable equilibrium point," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305841
    DOI: 10.1016/j.chaos.2020.110188
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    Cited by:

    1. Chen, Mo & Wang, Ankai & Wang, Chao & Wu, Huagan & Bao, Bocheng, 2022. "DC-offset-induced hidden and asymmetric dynamics in Memristive Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Zhang, Xiaohong & Xu, Jingjing & Moshayedi, Ata Jahangir, 2024. "Design and FPGA implementation of a hyperchaotic conservative circuit with initial offset-boosting and transient transition behavior based on memcapacitor," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    3. Xu, Wanjiang & Shi, Xuerong & Jiang, Haibo & Yu, Jianjiang & Zhang, Liping & Zhuang, Lizhou & Wang, Zuolei, 2024. "A simple 4D no-equilibrium chaotic system with only one quadratic term and its application in pseudo-random number generator," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Gong, Li-Hua & Luo, Hui-Xin & Wu, Rou-Qing & Zhou, Nan-Run, 2022. "New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 591(C).

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