Noise-assisted synchronization of the transition times of a set of uncoupled bistable elements

Abstract

We study the noise-induced synchronization of the transition times of a set of non-interacting bistable systems undergoing an activation process in the presence of an external periodic field. Starting from a collection of time series corresponding to these transition times, we first explore graphically the extent of the synchronization for different values of the noise intensity and the frequency of the periodic signal. Then we quantify this phenomenon by means of the fractional fluctuation of the transition times. We show that this quantity has an optimal behavior when we plot it as a function of the noise intensity and the frequency of the periodic external force. Three-dimensional plots of the fractional fluctuation versus these two parameters clearly exhibit the parameter region of optimal synchronization.