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Unidirectional synchronization of Hodgkin–Huxley neurons exposed to ELF electric field

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

Abstract

In this paper, a hybrid control strategy, H∞ variable universe adaptive fuzzy control, is derived and applied to synchronize two Hodgkin–Huxley (HH) neurons exposed to external electric field. Firstly, the modified model of HH neuron exposed to extremely low frequency (ELF) external electric field is established and its periodic and chaotic dynamics in response to sinusoidal electric field stimulation are described. And then the statement of the problem for unidirectional synchronization of two HH neurons is given. Finally H∞ variable universe adaptive fuzzy control is designed to synchronize the HH systems and the simulation results demonstrate the effectiveness of the proposed control method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:3:p:1335-1345
    DOI: 10.1016/j.chaos.2007.05.016
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    References listed on IDEAS

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    1. Cornejo-Pérez, Octavio & Femat, Ricardo, 2005. "Unidirectional synchronization of Hodgkin–Huxley neurons," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 43-53.
    2. Fotsin, Hilaire & Bowong, Samuel & Daafouz, Jamal, 2005. "Adaptive synchronization of two chaotic systems consisting of modified Van der Pol–Duffing and Chua oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 215-229.
    3. Xie, Lingli & Teo, Kok-lay & Zhao, Yi, 2007. "Chaos synchronization for continuous chaotic systems by inertial manifold approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 234-245.
    4. 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.
    5. 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.
    6. Czołczynski, K. & Perlikowski, P. & Stefański, A. & Kapitaniak, T., 2007. "Synchronization of self-excited oscillators suspended on elastic structure," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 937-943.
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