Phenomenological bifurcation in a generally stochastic population model with Allee effect.

A general population model with Allee effect driven by correlated additive and multiplicative white noises is considered. This paper aims to investigate noise-induced phenomenological bifurcation (P-bifurcation) and the influence of noises on the population model. With the help of Fokker-Planck equation, we obtain the stationary probability distribution (SPD) of the model, and find that the shape of SPD experiences a transition from one structure to another when the noise intensity passes through a critical value, i.e., the P-bifurcation occurs. Moreover, detailed analysis and simulations for stochastic logistic-like models with weak and strong Allee effects show that the correlated noises have complex effects on the eventual distribution of population size. This paper aims to investigate noise-induced phenomenological bifurcation (P-bifurcation) for a general population model with Allee effect driven by correlated additive and multiplicative white noises. We find that the shape of SPD experiences a transition from one structure to another when the noise intensity passes through a critical value, i.e., the P-bifurcation occurs.