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DC-offset-induced hidden and asymmetric dynamics in Memristive Chua's circuit

Author

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  • Chen, Mo
  • Wang, Ankai
  • Wang, Chao
  • Wu, Huagan
  • Bao, Bocheng

Abstract

Hidden attractors have been discovered in classical Chua's circuits with special Chua's diode nonlinearities. But designing such physical Chua's circuits is a challenge due to the distinct slopes of Chua's diodes. The analog-circuit-based measurements of hidden dynamical behaviors are also difficult since their attraction basins are relatively small and independent of any equilibrium points. In this paper, a DC-offset method is proposed for obtaining hidden dynamics from preexisting nonlinear circuits. An improved memristive Chua's circuit with hidden dynamical behaviors is constructed by inserting a DC voltage source into the inductor branch therein. The DC-offset-induced hidden and asymmetric dynamical behaviors are revealed via equilibrium point analyses, numerical simulations, and experimental measurements. The coexistence of hidden attractors is demonstrated when the modified memristive Chua's circuit possesses at least one unstable equilibrium point or only one stable equilibrium point. Furthermore, a reconstituted model is formulated using the incremental integral transformation method to facilitate the measurements of hidden and coexisting attractors having relatively small attraction basins. With this model, the self-excited and hidden properties of the coexisting attractors are maintained, while their attraction basins are transferred to the neighborhood of the easily circuit-implemented origin point. Thus, the existence of hidden and coexisting attractors is readily verified via hardware circuit measurements.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004027
    DOI: 10.1016/j.chaos.2022.112192
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    References listed on IDEAS

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    1. 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).
    2. Xu, Quan & Lin, Yi & Bao, Bocheng & Chen, Mo, 2016. "Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 186-200.
    3. Faradja, Philippe & Qi, Guoyuan, 2020. "Analysis of multistability, hidden chaos and transient chaos in brushless DC motor," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Jahanshahi, Hadi & Orozco-López, Onofre & Munoz-Pacheco, Jesus M. & Alotaibi, Naif D. & Volos, Christos & Wang, Zhen & Sevilla-Escoboza, R. & Chu, Yu-Ming, 2021. "Simulation and experimental validation of a non-equilibrium chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Alireza Yazdani & Lu Lu & Maziar Raissi & George Em Karniadakis, 2020. "Systems biology informed deep learning for inferring parameters and hidden dynamics," PLOS Computational Biology, Public Library of Science, vol. 16(11), pages 1-19, November.
    6. Wu, H. & Zhou, J. & Chen, M. & Xu, Q. & Bao, B., 2022. "DC-offset induced asymmetry in memristive diode-bridge-based Shinriki oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Liu, Tianming & Yan, Huizhen & Banerjee, Santo & Mou, Jun, 2021. "A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    8. 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.
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    Citations

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    Cited by:

    1. Gomes, Iacyel & Korneta, Wojciech & Stavrinides, Stavros G. & Picos, Rodrigo & Chua, Leon O., 2023. "Experimental observation of chaotic hysteresis in Chua's circuit driven by slow voltage forcing," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Wang, Ning & Cui, Mengkai & Yu, Xihong & Shan, Yufan & Xu, Quan, 2023. "Generating multi-folded hidden Chua’s attractors: Two-case study," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Yang, Feifei & Ma, Jun & An, Xinlei, 2022. "Mode selection and stability of attractors in Chua circuit driven by piezoelectric sources," Chaos, Solitons & Fractals, Elsevier, vol. 162(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. Chen, Mo & Xue, Wanqi & Luo, Xuefeng & Zhang, Yunzhen & Wu, Huagan, 2023. "Effects of coupling memristors on synchronization of two identical memristive Chua's systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Wang, Ning & Xu, Dan & Li, Ze & Xu, Quan, 2023. "A general configuration for nonlinear circuit employing current-controlled nonlinearity: Application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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