Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model

ABSTRACT Noise and time-delays are ubiquitous in physical and biological systems. In this paper, the multiple time-delays coupled FitzHugh-Nagumo (FHN) models is employed to investigate the synchronization mode transition. The orbital projection method is used to study the difference of membrane potential between two FHN neurons in the phase plane, and a measure of anti-phase is defined to characterize the synchronization state of neural system. It is shown that the synchronization mode of coupled neurons is different while changing the parameters of the system. In the absence of noise, as the coupling strength increases, the firing mode of two coupled neurons undergoes a succession of transitions (i.e., from the asynchronous state, to the completely synchronized state, then the anti-phase state, and finally to the completely synchronized state again). In the presence of noise, the synchronization mode of neurons becomes more diversified with the increasing of noise intensity. Moreover, by changing the time-delay and coupling strength, the sensitivity of two-neuron to noise can be changed, thereby the synchronization mode transition can be adjusted.