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Parallel bi-memristor hyperchaotic map with extreme multistability

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  • Bao, H.
  • Gu, Y.
  • Xu, Q.
  • Zhang, X.
  • Bao, B.

Abstract

Discrete memristors can be used to construct chaotic and hyperchaotic mapping models by self-feedback or coupling method, but these constructed maps do not have multistability or extreme multistability. Towards this end, by connecting two identical discrete memristors in parallel, this paper presents a novel parallel bi-memristor hyperchaotic map using the self-feedback method. This map has a plane fixed point set and its stability is entirely determined by memristor initial states. The control parameters-reliant hyperchaotic behaviors and the initial states-reliant coexisting behaviors are disclosed using several numerical methods. Complex dynamical behaviors closely relative to memristor and non-memristor initial states are demonstrated, indicating the occurrence of extreme multistability. Besides, a digital hardware platform is developed and the experimental results are captured to well validate the numerical ones. Consequently, the presented parallel bi-memristor map can display hyperchaotic dynamics and it is flexible to show extreme multistability.

Suggested Citation

  • Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004830
    DOI: 10.1016/j.chaos.2022.112273
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    6. Grime, Gabriel C. & Roberto, Marisa & Viana, Ricardo L. & Elskens, Yves & Caldas, Iberê L., 2023. "Biquadratic nontwist map: a model for shearless bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
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