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

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.