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

Hu Wang, Sha Wang (), Yajuan Gu and Yongguang Yu
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Hu Wang: School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
Sha Wang: School of Information, Beijing Wuzi University, Beijing 101149, China
Yajuan Gu: School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
Yongguang Yu: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2023, vol. 11, issue 3, 1-17

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.

Keywords: Hodgkin–Huxley model; simplified model; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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