PROBABILITY DENSITIES FOR NOISY DELAY BIFURCATIONS

Abstract

The delay of a transition in a nonlinear system due to a slowly varying control parameter can be significantly reduced by very small noise. A new asymptotic approximation for the time-dependent probability density function gives a complete description of the process into the transition region, and is easily interpreted in terms of the noisy dynamics. It is also used to calculate mean transition times. The method is applied to two nonlinear systems with noise: a one-dimensional canonical model for a steady bifurcation and the noisy FitzHugh–Nagumo model.