Phenomenological bifurcation in a stochastic logistic model with correlated colored noises

A stochastic logistic model with correlated colored noises is proposed and investigated. First, we derive an approximative Fokker-Planck equation for the stochastic model and solve its steady-state solution, i.e., the stationary probability distribution (SPD) of the stochastic model. By performing detailed structural analysis for the SPD, we find that the phenomenological bifurcation may occur in the stochastic model. In other words, the shape of SPD will experience a transition from one structure to another as the feasible parameter passes through a critical value. In addition, the effects of correlation degree and correlation time of the noises on the bifurcation diagram are also analyzed. (C) 2019 Elsevier Ltd. All rights reserved.