Noise-induced extinction in Bazykin-Berezovskaya population model

Abstract

A nonlinear Bazykin-Berezovskaya prey-predator model under the influence of parametric stochastic forcing is considered. Due to Allee effect, this conceptual population model even in the deterministic case demonstrates both local and global bifurcations with the change of predator mortality. It is shown that random noise can transform system dynamics from the regime of coexistence, in equilibrium or periodic modes, to the extinction of both species. Geometry of attractors and separatrices, dividing basins of attraction, plays an important role in understanding the probabilistic mechanisms of these stochastic phenomena. Parametric analysis of noise-induced extinction is carried out on the base of the direct numerical simulation and new analytical stochastic sensitivity functions technique taking into account the arrangement of attractors and separatrices.