Self-organized localization of macrostates by additive noise in a fast-slow dynamical system: effect of the slow nonreactive mode on the barrier crossing rate of the fast, bistable mode

Abstract

We have studied the stochastic dynamics of a two-dimensional gradient system composed of a fast, bistable mode and a slow, monotonically decaying mode. The coupling is bidirectional and cooperative. Additive white noise acts on the fast mode only. We find that the noise intensity controls the location of macrostates (shape of the probability density function), the appearance of bimodality in the slow-mode probability distribution and, together with the coupling strength, the rate of fast-mode barrier crossing. These features arise from the interplay of noise, widely separated time scales, and bidirectional, excitatory coupling. They are believed to be generic.