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Hopf Bifurcation Analysis of a Two-Dimensional Simplified Hodgkin–Huxley Model

Author

Listed:
  • Hu Wang

    (School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China)

  • Sha Wang

    (School of Information, Beijing Wuzi University, Beijing 101149, China)

  • Yajuan Gu

    (School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China)

  • Yongguang Yu

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

This paper presents a two-dimensional simplified Hodgkin–Huxley model under exposure to electric fields. The Hopf bifurcations of the simplified Hodgkin–Huxley model are investigated through qualitative analysis and numerical simulations. A necessary and sufficient condition for the existence of Hopf bifurcations is derived, and the conditions for supercritical and subcritical Hopf bifurcations are obtained. Finally, bifurcation diagrams are given for two parameters, and numerical examples are presented to illustrate the effectiveness of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:717-:d:1052695
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    References listed on IDEAS

    as
    1. Baysal, Veli & Yılmaz, Ergin, 2021. "Chaotic Signal Induced Delay Decay in Hodgkin-Huxley Neuron," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. André H. Erhardt, 2018. "Bifurcation Analysis of a Certain Hodgkin-Huxley Model Depending on Multiple Bifurcation Parameters," Mathematics, MDPI, vol. 6(6), pages 1-15, June.
    3. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Bifurcation control of the Hodgkin–Huxley equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 217-224.
    4. Che, Yan-Qiu & Wang, Jiang & Si, Wen-Jie & Fei, Xiang-Yang, 2009. "Phase-locking and chaos in a silent Hodgkin–Huxley neuron exposed to sinusoidal electric field," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 454-462.
    5. Shaolong Li & Weipeng Lv & Zhenyang Chen & Miao Xue & Qinsheng Bi, 2022. "Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model," Mathematics, MDPI, vol. 10(23), pages 1-21, December.
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