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Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems

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  • Yu, Hongjie
  • Peng, Jianhua

Abstract

A new approach for chaotic synchronization of Hindmarsh–Rose (HR) neural networks linked by special nonlinear coupling function is proposed. The method expands SC method in investigation of chaotic synchronization based on the stability criterion. We provide the error evolutional equation to determine the stability of synchronized states, which has very simple forms corresponding to matrix of star coupling coefficients. The synchronization can be achieved without the requirement to calculate the maximum Lyapunov exponents when the coupling strengths are taken as reference values, and there is a region of stability around them. Besides, the stability criterion control method is applied to control chaotic behaviors of individual Hindmarsh–Rose neuron model. The chaotic orbit is stabilized on 5spike/burst orbit embedded in the chaotic attractor by an input of the nonlinear time-continuous feedback perturbation to membrane potential.

Suggested Citation

  • Yu, Hongjie & Peng, Jianhua, 2006. "Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 342-348.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:2:p:342-348
    DOI: 10.1016/j.chaos.2005.08.075
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    Cited by:

    1. Wang, Jiang & Che, Yan-Qiu & Zhou, Si-Si & Deng, Bin, 2009. "Unidirectional synchronization of Hodgkin–Huxley neurons exposed to ELF electric field," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1335-1345.
    2. Sabouri, Amir & Ghasemi, Mahdieh & Mehrabbeik, Mahtab, 2023. "The dynamical analysis of non-uniform neocortical network model in up-down state oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Wang, Jiang & Chen, Lisong & Deng, Bin, 2009. "Synchronization of Ghostburster neuron in external electrical stimulation via H∞ variable universe fuzzy adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2076-2085.
    4. Branislav Rehák & Volodymyr Lynnyk, 2021. "Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    5. Sun, Li & Wang, Jiang & Deng, Bin, 2009. "Global synchronization of two Ghostburster neurons via active control," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1213-1220.
    6. Wang, Jiang & Zhang, Zhen & Li, Huiyan, 2008. "Synchronization of FitzHugh–Nagumo systems in EES via H∞ variable universe adaptive fuzzy control," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1332-1339.
    7. Fang, Xiao-Ling & Yu, Hong-Jie & Jiang, Zong-Lai, 2009. "Chaotic synchronization of nearest-neighbor diffusive coupling Hindmarsh–Rose neural networks in noisy environments," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2426-2441.
    8. Bonacini, E. & Burioni, R. & di Volo, M. & Groppi, M. & Soresina, C. & Vezzani, A., 2016. "How single node dynamics enhances synchronization in neural networks with electrical coupling," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 32-43.
    9. Erjaee, G.H., 2009. "Numerical stability of chaotic synchronization using a nonlinear coupling function," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 682-688.
    10. Hou, Zhangliang & Ma, Jun & Zhan, Xuan & Yang, Lijian & Jia, Ya, 2021. "Estimate the electrical activity in a neuron under depolarization field," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    11. Jia, Chenhui & Wang, Jiang & Deng, Bin, 2009. "How the self-coupled neuron can affect the chaotic synchronization of network," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1112-1119.
    12. Burić, Nikola & Todorović, Kristina & Vasović, Nebojša, 2009. "Exact synchronization of noisy bursting neurons with coupling delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1127-1135.
    13. Vieira, Robson & Martins, Weliton S. & Barreiro, Sergio & Oliveira, Rafael A. de & Chevrollier, Martine & Oriá, Marcos, 2021. "Synchronization of a nonlinear oscillator with a sum signal from equivalent oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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