Spatiotemporal characteristics in systems of diffusively coupled excitable slow-fast FitzHugh-Rinzel dynamical neurons

TL;DR

This paper analyzes the formation of complex spatiotemporal patterns, including spirals and antispirals, in a diffusively coupled FitzHugh-Rinzel neuron model, revealing insights into neural excitability and wave dynamics.

Contribution

It provides analytical conditions for pattern formation near Hopf bifurcations and explores diverse neural responses in 1D and 2D configurations.

Findings

Derives amplitude equation coefficients near Hopf bifurcations.

Identifies conditions for antispiral and spiral wave formation.

Shows collective behavior in coupled systems with varied firing characteristics.

Abstract

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the formation of spatiotemporal patterns. We focus on local, nonlinear excitations and diverse neural responses in an excitable 1- and 2-dimensional configuration of diffusively coupled FitzHugh-Rinzel neurons. The study of the emerging spatiotemporal patterns is essential in understanding the working mechanism in different brain areas. We derive analytically the coefficients of the amplitude equations in the vicinity of Hopf bifurcations and characterize various patterns, including spirals exhibiting complex geometric substructures. Further, we derive analytically the condition for the development of antispirals in the neighborhood of the bifurcation point. The emergence of broken target waves can be observed to form spiral-like profiles. The spatial dynamics of the excitable system exhibits 2- and multi-arm spirals for small diffusive couplings. Our results reveal a multitude of neural excitabilities and possible conditions for the emergence of spiral-wave formation. Finally, we show that the coupled excitable systems with different firing characteristics, participate in a collective behavior that may contribute significantly to irregular neural dynamics.