Qualitative Analysis of certain Reaction-Diffusion Systems of the FitzHugh-Nagumo type
Dynamical Systems
2023-04-05 v3
Abstract
This article aims to provide insights into the qualitative analysis of some nonlinear Reaction-Diffusion (RD) systems arising in Neuroscience. We first introduce a non-homogeneous FitzHugh-Nagumo (nhFHN) featuring excitability and oscillatory properties. Then, we discuss the qualitative analysis of a toy model related to nhFHN. In particular, we focus on the convergence of solutions of the toy model toward different solutions (fixed point, periodic) and show the existence of a cascade of Hopf bifurcations. Finally, we connect this analysis to the nhFHN system.
Keywords
Cite
@article{arxiv.1903.05754,
title = {Qualitative Analysis of certain Reaction-Diffusion Systems of the FitzHugh-Nagumo type},
author = {Benjamin Ambrosio},
journal= {arXiv preprint arXiv:1903.05754},
year = {2023}
}