Dynamic effects of time delay on a coupled FitzHugh–Nagumo neural system

Abstract

In this paper, a coupled FitzHugh–Nagumo (FHN) neural system with time delay has been proposed and its stability and Hopf bifurcation are researched. Specifically, the stability of equilibrium point is analyzed by employing the corresponding characteristic equation. Sufficient conditions for existence of Hopf bifurcation are obtained. The results show that the FHN neural system exhibits the parameter regions involved the delay-independence stability and delay dependence stability. Increase of time delay can induce the stability switches between resting state and periodic activity. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.