Dynamical Computations of the FitzHugh- Nagumo Equation

Abstract

The Hodgin-Huxley model is one of the most widely studied biological systems of nonlinear differential equations that is applied to explore nerve cells activities via electrical communications. In this paper we consider some numerical aspects of a simplifi ed version of this model known as the FitzHugh-Nagumo (FHN) equation. Dynamical experiments conducted herein not only confi rm those obtained from earlier studies but also facilitate a better understanding of the qualitative features of the FHN model especially those that initiate the behavior a threshold-triggered excitation media. To this end, methods of dynamical system analysis such as bifurcation and linear stability analysis are deployed to investigate the general qualitative features of an inhibitor-activator system which characterizes the FHN system of equations. Research Article Dynamical Computations of the FitzHughNagumo Equation Okey Oseloka Onyejekwe* The Robnello Unit for Continuum Mechanics Applications and Nonlinear Dynamics, Umuagu, Oshimili South, Asaba, Delta State, Nigeria Received: 16 August , 2021 Accepted: 31 August , 2021 Published: 01 September, 2021 *Corresponding author: Okey Oseloka Onyejekwe, The Robnello Unit for Continuum Mechanics Applications and Nonlinear Dynamics, Umuagu, Oshimili South, Asaba, Delta State, Nigeria, E-mail: