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Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis

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  • Zhang, Yunzhen
  • Liu, Zhong
  • Wu, Huagan
  • Chen, Shengyao
  • Bao, Bocheng

Abstract

This paper presents a two-memristor-based chaotic system by introducing two memristors into an existing chaotic jerk system. Such a memristive system possesses plane equilibrium therein, leading to the emergence of extreme multistability. Due to the existence of two zero eigenvalues for the plane equilibrium, it is extremely difficult to quantitatively explore the dynamical mechanism based on the original system model. For this reason, an equivalent dimensionality reduction model is obtained using state variable mapping (SVM) method. Consequently, the initials-dependent extreme multistability in the two-memristor-based chaotic system is reconstituted by the initial parameters-related dynamics in the dimensionality reduction model, upon which the exact prediction, analysis and control of extreme multistability is thereby executed through traditional quantitative analyses. Furthermore, PSIM circuit simulations based on a physical circuit are performed to confirm the extreme multistability. It is demonstrated that the initials-dependent extreme multistability can be reconstituted through dimensionality reduction analysis, which is efficient for exploring the inner mechanisms and further seeking possible applications of this special phenomenon.

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  • Zhang, Yunzhen & Liu, Zhong & Wu, Huagan & Chen, Shengyao & Bao, Bocheng, 2019. "Two-memristor-based chaotic system and its extreme multistability reconstitution via dimensionality reduction analysis," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 354-363.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:354-363
    DOI: 10.1016/j.chaos.2019.07.004
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    Cited by:

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    2. 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).
    3. Bao, B. & Peol, M.A. & Bao, H. & Chen, M. & Li, H. & Chen, B., 2021. "No-argument memristive hyper-jerk system and its coexisting chaotic bubbles boosted by initial conditions," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Peng, Yuexi & Sun, Kehui & He, Shaobo, 2020. "A discrete memristor model and its application in Hénon map," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    6. Chen, Mo & Ren, Xue & Wu, Huagan & Xu, Quan & Bao, Bocheng, 2020. "Interpreting initial offset boosting via reconstitution in integral domain," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Ahmadi, Atefeh & Parthasarathy, Sriram & Natiq, Hayder & Jafari, Sajad & Franović, Igor & Rajagopal, Karthikeyan, 2023. "A non-autonomous mega-extreme multistable chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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