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A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability

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  • Zhang, Sen
  • Zheng, Jiahao
  • Wang, Xiaoping
  • Zeng, Zhigang

Abstract

In this paper, a novel no-equilibrium Hindmarsh-Rose (HR) neuron model with memristive electromagnetic induction is proposed. This memristive HR neuron model exhibits complex memristor initial offset boosting dynamics, from which infinitely many coexisting hidden attractors sharing the same shape but with different positions can be generated, therefore breeding the interesting phenomenon of hidden homogeneous extreme multistability. The complicated dynamical behaviors are detailedly investigated via bifurcation diagrams, Lyapunov exponents, time series, attraction basins and spectral entropy (SE) complexity. Moreover, PSIM circuit simulations and DSP hardware experiments are carried out to demonstrate the theoretical analyses and numerical simulations. Finally, a pseudorandom number generator is also designed by using the memristor initial-controlled chaotic sequences extracted from the memristive HR neuron model. The performance analysis results show that these chaotic sequences can yield pseudorandom numbers with excellent randomness, which are more suitable for chaos-based engineering applications.

Suggested Citation

  • Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001132
    DOI: 10.1016/j.chaos.2021.110761
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    Cited by:

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    5. 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).
    6. Qing Ding & Oumate Alhadji Abba & Hadi Jahanshahi & Madini O. Alassafi & Wen-Hua Huang, 2022. "Dynamical Investigation, Electronic Circuit Realization and Emulation of a Fractional-Order Chaotic Three-Echelon Supply Chain System," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    7. Tabekoueng Njitacke, Zeric & Tsafack, Nestor & Ramakrishnan, Balamurali & Rajagopal, Kartikeyan & Kengne, Jacques & Awrejcewicz, Jan, 2021. "Complex dynamics from heterogeneous coupling and electromagnetic effect on two neurons: Application in images encryption," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    8. Yan, Shaohui & Wang, Ertong & Gu, Binxian & Wang, Qiyu & Ren, Yu & Wang, Jianjian, 2022. "Analysis and finite-time synchronization of a novel double-wing chaotic system with transient chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    9. Li, Kexin & Bao, Bocheng & Ma, Jun & Chen, Mo & Bao, Han, 2022. "Synchronization transitions in a discrete memristor-coupled bi-neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    10. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. 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).
    12. Yamina Soula & Hadi Jahanshahi & Abdullah A. Al-Barakati & Irene Moroz, 2023. "Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    13. 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).
    14. Ding, Dawei & Chen, Xiaoyu & Yang, Zongli & Hu, Yongbing & Wang, Mouyuan & Zhang, Hongwei & Zhang, Xu, 2022. "Coexisting multiple firing behaviors of fractional-order memristor-coupled HR neuron considering synaptic crosstalk and its ARM-based implementation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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