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Bifurcation control of the Hodgkin–Huxley equations

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  • Wang, Jiang
  • Chen, Liangquan
  • Fei, Xianyang

Abstract

The Hodgkin–Huxley equations (HH) are parameterized by a number of parameters and show a variety of qualitatively different behaviors. This paper finds that when the externally applied current Iext varies the bifurcation would occur in the HH equations. The HH model’s Hopf bifurcation is controlled by permanent or interval Washout filters (WF), which can transform the subcritical bifurcations into supercritical bifurcations, and can make the HH equations stable directly. Simulation results show the validity of those controllers. We choose the membrane voltage V as an input to the washout filter because V can be readily measured, and the controller can be realized easily. The controller designs described here may boost the development of electrical stimulation systems for patients suffering from different neuron-system dysfunctions.

Suggested Citation

  • Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Bifurcation control of the Hodgkin–Huxley equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 217-224.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:217-224
    DOI: 10.1016/j.chaos.2006.01.035
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    References listed on IDEAS

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    Cited by:

    1. Hu Wang & Sha Wang & Yajuan Gu & Yongguang Yu, 2023. "Hopf Bifurcation Analysis of a Two-Dimensional Simplified Hodgkin–Huxley Model," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
    2. Doruk, Resat Ozgur, 2013. "Control of repetitive firing in Hodgkin–Huxley nerve fibers using electric fields," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 66-72.
    3. Che, Yanqiu & Liu, Bei & Li, Huiyan & Lu, Meili & Wang, Jiang & Wei, Xile, 2017. "Robust stabilization control of bifurcations in Hodgkin-Huxley model with aid of unscented Kalman filter," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 92-99.
    4. Zheng, Hongyu & Luo, Xiaoshu, 2009. "Optimal synchronization in small-world biological neural networks with time-varying weights," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 516-520.

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