Analysis of Turing Instability of the Fitzhugh-Nagumo Model in Diffusive Network

Abstract

This study mainly investigates the dynamical analysis of the FitzHugh-Nagumo (FHN) neuron model. Firstly, it analyzes the equilibrium stability of the system in the absence of network diffusion. Then, it considers two types of network topologies: random networks and higher-order networks. The paper analyzes the Turing instability phenomenon in the presence of network diffusion, identifies the critical diffusion coefficient in the FHN model that leads to Turing instability, and plots the eigenvalue distribution diagram, known as the Turing pattern. The research findings indicate that networks with higher-order connections, as opposed to random networks, display a more intricate interplay among neurons. This heightened interconnection intensifies the Turing instability phenomenon, amplifying its significance within the system. The stability of the dynamical system can be associated with the onset of neurological disorders such as epilepsy, caused by abnormal neuronal firing. This analogy facilitates the transfer of content related to the instability of control systems to the regulation of neurological disorders.