Combined impacts of the Allee effect, delay and stochasticity: Persistence analysis

Abstract

We study a combined influence of the Allee effect, delay and stochasticity on the base of the phenomenological Hassell mathematical model of population dynamics. This bistable dynamical model possesses a wide variety of regimes, both regular and chaotic. In the persistence zone, these regimes coexist with the trivial equilibrium that corresponds to the extinction of the population. It is shown that borders of the persistence zone are defined by the crisis and saddle-node bifurcation points. Noise-induced transitions from the persistence to the extinction are studied both numerically and analytically. Using numerical modeling, we have found that the persistence zone can decrease and even disappear under the influence of random noise. For the theoretical study of this phenomenon, we apply the stochastic sensitivity analysis and Mahalanobis metrics.