Bifurcation Analysis of the Hodgkin-Huxley Model Exposed to External DC Electric Field

Abstract

Based on the modified Hodgkin-Huxley (HH) model exposed to extremely low frequency (ELF) electric field, we study Hopf and saddle-node bifurcations of the modified HH model in two dimensional parameter space of externally applied DC current and trans-membrane voltage induced by external DC electric field. The bifurcation sets are calculated by employing the generalized algebra criterion in high dimensional system. The obtained bifurcation sets partition the two dimensional parameter space in terms of the qualitatively different behaviors of the HH model. Thus the neuron's information encodes the stimulus information, and vice versa, which is significant in neuron control. The study is of some biological significance and suggest that the aberration of dynamics in bio-systems may account for diseases caused by electric exposure.