Analysis of hopf bifurcation in the hodgkin-Huxley model exposed to external DC electric field

Based on the Hodgkin-Huxley(HH) model,we analyze the mechanism of external DC electric field effect onto neuron,and establish the modified Hodgkin-Huxley model.We calculate the Hopf bifurcation sets of one-parameter space of(externally applied DC current) and(induced trans-membrane voltage by external DC electric field) by employing the generalized algebra criterion of the existence of Hopf bifurcation in high dimensional system,and parameter regions in which the stable periodic solutions of the modified HH model exist are obtained.The researches are of some biological significance and suggest that the aberration of dynamics in bio-systems may account for diseases caused by electric exposure.