Analysis of stochastic phenomena in Ricker-type population model with delay

Abstract

A phenomenon of the noise-induced extinction is studied on the base of the conceptual Ricker-type model with the delay and Allee effect. This nonlinear discrete population model exhibits the persistence with the different form of attractors, both regular and chaotic. For this model, the persistence zones are defined by points of the crisis bifurcations. The phenomenon of the noise-induced extinction is investigated with the help of direct numerical simulations and by the semi-analytical new method based on the stochastic sensitivity functions. In the stochastic analysis, a geometrical approach taking into account a mutual arrangement of the confidence domains and basins of attraction is used.