The FitzHugh–Nagumo Model Described by Fractional Difference Equations: Stability and Numerical Simulation

Abstract

The aim of this work is to describe the dynamics of a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for the local asymptotic stability of the system’s unique equilibrium. Moreover, we employed a Lyapunov functional to show that the constant equilibrium solution is globally asymptotically stable. Furthermore, numerical simulations are shown to clarify and exemplify the theoretical results.

Keywords

• fractional discrete reaction–diffusion equations
• FitzHugh–Nagumo model
• global asymptotic stability
• Lyapunov functional