Influence of white noise on delayed bifurcations

Abstract

We analyze the time-dependent solution of the simplest Fokker-Planck equation which describes the action of Gaussian white noise in a single-mode laser. The pump parameter is linearly swept in time. Because of the critical slowing down, the time evolution of the probability distribution exhibits a delay with respect to the instantaneous value of the pump parameter. The delay turns out to depend crucially on the sweeping rate and to be essentially independent of the initial value of the swept parameter.