Non trivial dynamics in the FizHugh-Rinzel model and non-homogeneous oscillatory-excitable reaction-diffusions systems

TL;DR

This paper explores complex dynamics in the FitzHugh-Rinzel model and non-homogeneous FitzHugh-Nagumo reaction-diffusion systems, revealing phenomena like canards, mixed mode oscillations, and bifurcations relevant to neuroscience.

Contribution

It provides new insights into the complex behaviors of these models, linking them to wave propagation phenomena in neuroscience.

Findings

Identification of canards and mixed mode oscillations in the models

Demonstration of Hopf bifurcations in the system dynamics

Relevance of these dynamics to neural wave propagation

Abstract

In this article, we discuss the dynamics of the 3-dimensional FitzHugh-Rinzel (FHR) model and a class of non-homogeneous FitzHugh-Nagumo (Nh-FHN) Reaction-Diffusion systems. The Nh-FHN models can be used to generate relevant wave propagation phenomena in Neuroscience context. This gives raise locally to complex dynamics such as canards, Mixed Mode Oscillations, Hopf-Bifurcations some of which can be observed in the FHR model.