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Two-parameters Hopf bifurcation in the Hodgkin–Huxley model

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  • Wang, Jiang
  • Geng, Jianming
  • Fei, Xiangyang

Abstract

In this paper, the Hodgkin–Huxley model is studied with the leakage conductance and the sodium reversal potential selected as parameters for a two-parameter Hopf-bifurcation analysis. The influence of bifurcation on the HH model was also discussed and algebra criterion in high dimension equations was used to identify Hopf bifurcation. In addition, this paper also discuses the bifurcation approach to inherited disorders of ion channels in skeletal muscle excitable membranes.

Suggested Citation

  • Wang, Jiang & Geng, Jianming & Fei, Xiangyang, 2005. "Two-parameters Hopf bifurcation in the Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 973-980.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:3:p:973-980
    DOI: 10.1016/j.chaos.2004.06.061
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    Cited by:

    1. Han, Chunxiao & Wang, Jiang & Deng, Bin, 2009. "Fire patterns of modified HH neuron under external sinusoidal ELF stimulus," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2045-2054.
    2. He, Ji-Huan, 2006. "A modified Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 303-306.
    3. Wang, P.K.C. & Kogan, B.Y., 2007. "Parametric study of the Noble’s action potential model for cardiac Purkinje fibers," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1048-1063.

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