Escape statistics for systems driven by dichotomous noise. II. The imperfect pitchfork bifurcation as a case study

Abstract

We use the general results for the escape probabilities and mean exit times obtained in an accompanying paper to analyze in detail a nonlinear system presenting an imperfect (subcritical) pitchfork bifurcation. We redraw the bifurcation diagram to show the effect of the noise. To avoid spurious results we introduce the concept ofextinction level as the minimum possible value for the system, and discuss its effect on the bifurcation diagram.