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Robust synchronization control of coupled chaotic neurons under external electrical stimulation

Author

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  • Che, Yan-Qiu
  • Wang, Jiang
  • Zhou, Si-Si
  • Deng, Bin

Abstract

In this paper, a robust adaptive neural network (NN) controller is proposed to realize the synchronization of two gap junction coupled chaotic FitzHugh–Nagumo (FHN) neurons under external electrical stimulation. Based on the Lyapunov stability theory, we derive the update laws of NN for approximating the nonlinear uncertain functions of the error dynamical system. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.

Suggested Citation

  • Che, Yan-Qiu & Wang, Jiang & Zhou, Si-Si & Deng, Bin, 2009. "Robust synchronization control of coupled chaotic neurons under external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1333-1342.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1333-1342
    DOI: 10.1016/j.chaos.2007.09.014
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    References listed on IDEAS

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    1. Wang, Jiang & Deng, Bin & Fei, Xiangyang, 2006. "Chaotic synchronization of two coupled neurons via nonlinear control in external electrical stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1272-1278.
    2. Cornejo-Pérez, Octavio & Femat, Ricardo, 2005. "Unidirectional synchronization of Hodgkin–Huxley neurons," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 43-53.
    3. Zhang, Ting & Wang, Jiang & Fei, Xiangyang & Deng, Bin, 2007. "Synchronization of coupled FitzHugh–Nagumo systems via MIMO feedback linearization control," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 194-202.
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    Cited by:

    1. Faedo, Nicolás & García-Violini, Demián & Ringwood, John V., 2021. "Controlling synchronization in a complex network of nonlinear oscillators via feedback linearisation and H∞-control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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