Gröbner basis method in FitzHugh-Nagumo model

Abstract

The FitzHugh-Nagumo model is a two dimensional system of differential equations with polynomial right-hand sides. The model describes an excitable system and explains basic phenomena in dynamics of neuron activity, for example spike generations in a neuron after stimulation by external current input. The system is slow-fast, meaning system with different time scales for each state variable. We analyse bifurcation manifolds of the FitzHugh-Nagumo system in whole parameter space using algebraic approach based on Gröbner basis.