# Propagation of bursting oscillations in coupled Hodgkin-Huxley Reaction-Diffusion systems

## TL;DR

This paper develops a mathematical framework for Hodgkin-Huxley reaction-diffusion networks, demonstrating solution properties and analyzing the propagation of bursting oscillations through coupled systems with bifurcation phenomena.

## Contribution

It introduces a general mathematical framework for Hodgkin-Huxley reaction-diffusion systems, proving existence, uniqueness, and invariant regions, and explores oscillation propagation and bifurcations.

## Key findings

- Existence and uniqueness of solutions established.
- Propagation of bursting oscillations demonstrated.
- Bifurcation phenomena observed in coupled systems.

## Abstract

We consider networks of reaction-diffusion systems of Hodgkin-Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as existence of invariant regions and of the attractor. Then, we illustrate some relevant numerical examples and exhibit bifurcation phenomena and propagation of bursting oscillations through one and two coupled systems.