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Multi-parameter Hopf-bifurcation in Hodgkin–Huxley model exposed to ELF external electric field

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  • Jiang, Wang
  • Yanqiu, Che
  • Xiangyang, Fei
  • Li, Li

Abstract

The interference between external electric exposure and biological objects is discussed. Based on results of space–time characteristics of trans-membrane voltage, the variation of cell trans-membrane voltage exposed to extremely low frequency (ELF) electric field is analyzed; a modified Hodgkin–Huxley (HH) model is established by introducing a new parameter denoting the effect of external electric field, and the bifurcation caused by the new parameter as well as leakage conductance and sodium ions anti-electromotive force is studied. The algebra criterion in high dimension equations is employed to perform the analysis of multi-parameter dynamical bifurcation. The results are of biological significance and suggest that the aberration of dynamics in bio-systems may account for diseases caused by electric exposure.

Suggested Citation

  • Jiang, Wang & Yanqiu, Che & Xiangyang, Fei & Li, Li, 2005. "Multi-parameter Hopf-bifurcation in Hodgkin–Huxley model exposed to ELF external electric field," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1221-1229.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:4:p:1221-1229
    DOI: 10.1016/j.chaos.2005.02.042
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    Citations

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    Cited by:

    1. He, Ji-Huan, 2006. "A modified Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 303-306.
    2. 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.
    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. Wang, Jiang & Zhang, Ting & Che, Yanqiu, 2007. "Chaos control and synchronization of two neurons exposed to ELF external electric field," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 839-850.
    5. 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.
    6. Wang, Jiang & Si, Wenjie & Che, Yanqiu & Fei, Xiangyang, 2008. "Spike trains in Hodgkin–Huxley model and ISIs of acupuncture manipulations," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 890-900.
    7. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Analysis and control of the bifurcation of Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 247-256.

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