Chaotic oscillations in singularly perturbed FitzHugh-Nagumo systems

TL;DR

This paper studies chaotic oscillations in singularly perturbed FitzHugh-Nagumo systems, showing how their dynamics can be reduced to a one-dimensional map and analyzing chaos emergence through numerical methods.

Contribution

It introduces a numerical scheme for the one-dimensional map governing the system and explores chaos in parameter variations, extending previous bifurcation studies.

Findings

Dynamics governed by a one-dimensional map

Numerical scheme for Lyapunov exponent computation

Identification of chaos routes in parameter space

Abstract

We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to accurately compute it together with its Lyapunov exponent. We then investigate the occurrence of chaos by varying the parameters of the system, with especial emphasis on the simplest possible chaotic oscillations. Our results corroborate and complement some recent works on bifurcations and routes to chaos in certain particular cases corresponding to piecewise linear FitzHugh-Nagumo-like systems.