Phase Diagrams of Noise Induced Transitions: Exact Results for a Class of External Coloured Noise

Abstract
By using the formula for the steady state probability distribution of fluctuation in a nonlinear systems under the influence of two-level Markovian noise, the existence of phase transitions of such a system with the variation of intensity and correlation time of the noise is shown. Explicit results for the Verhulst model and a model for population genetics are given and compared with the previous results for the white noise case.