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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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    1. Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    2. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    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. 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.
    5. Mo Chen & Yang Feng & Han Bao & Bocheng Bao & Huagan Wu & Quan Xu, 2019. "Hybrid State Variable Incremental Integral for Reconstructing Extreme Multistability in Memristive Jerk System with Cubic Nonlinearity," Complexity, Hindawi, vol. 2019, pages 1-16, June.
    6. Chen, M. & Feng, Y. & Bao, H. & Bao, B.C. & Yu, Y.J. & Wu, H.G. & Xu, Q., 2018. "State variable mapping method for studying initial-dependent dynamics in memristive hyper-jerk system with line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 313-324.
    7. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    8. Guangyi Wang & Chuanbao Shi & Xiaowei Wang & Fang Yuan, 2017. "Coexisting Oscillation and Extreme Multistability for a Memcapacitor-Based Circuit," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-13, January.
    9. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
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    Cited by:

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    2. 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).

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