Flow curvature in a self-coupled FitzHugh-Nagumo model

Abstract

In this paper we consider a self-coupled FitzHugh-Nagumo model describes a prototype of an excitable system (e.g., a neuron). The aim is to construct the expansion of invariant manifold with variable stability and corresponding gluing function using flow curvature method. We show that a self-coupled FitzHugh-Nagumo model has sufficiently smooth invariant surface, called “black swan”. Computer simulation and computer algebra methods are used for the quantitative analysis of the model.