Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model

Abstract

Noise and time delay are ubiquitous in various physical and biological systems. In this paper, we studied the phase synchronization and mode transition of oscillation mode induced by time delays and noises in a coupled FitzHugh–Nagumo (FHN) neural system. In the case of coupled neurons with single time delay, it is found that the mode oscillation of neurons induced by the noise and time delay undergoes a successive transitions from the synchronization, the out-of phase, the alternating phase-drift and anti-phase state, to the anti-phase state. In the case of coupled neurons with two time delays, when the two delays are comparable, the large amplitude oscillation of potential is in alternating synchronous and asynchronous state in the absence of noises, and the small amplitude oscillation of potential is always synchronized. The oscillation behaviors of coupled neurons with two time delays are similar to the cases with a single time delay in the presence of noises. When one of two time delays is largely dominant over the other, the neurons show completely different dynamic behaviors.