Definition, stability analysis and numerical simulation of FitzHugn-Nagumo model

Abstract

In this paper, the definition, nonlinear mechanism and numerical analysis of FitzHugn-Nagumo model are introduced. FitzHugn-Nagumo model is used to describe the action potential and recovery process of neurons. In this paper, the definition of FitzHugn-Nagumo model [1] is first given. FitzHugn-Nagumo model is used to describe the action potential and recovery process of neurons. In this paper, the nonlinear mechanism of the model is considered, the fixed point of the model is calculated, the linear stability of the model is analyzed, the characteristic value of the model and the system behavior are analyzed, and the formation mechanism of Hopf bifurcation, critical conditions and limit cycles are discussed. The Euler method, the most commonly used numerical algorithm, is used to visually discuss the system behavior, and the rationality and validity of FitzHugn-Nagumo model are verified, which provides an important reference for the study of neuronal dynamics.