Population system with coupling between non-Gaussian and Gaussian colored noise under Allee effect

Abstract

We investigate a stochastic model for single species population growth with strong and weak Allee effects subjected to coupling between non-Gaussian and Gaussian colored noise as well as nonzero cross-correlation in between. Stationary probability distribution of population model is obtained depending on the Fokker–Planck equation. The mean first-passage time is also calculated in order to quantify the time of transition between survival state and extinction state with Allee effect in population. The intensity of non-Gaussian colored noise can induce phase transition, and population may be vulnerable to extinction due to the increase in the intensity of non-Gaussian colored noise. Whether Allee effect is strong or weak, the increase in Allee threshold will not contribute to the survival and stability of the population. Further, the phenomenon of resonant activation is firstly discovered in the study of population dynamics with Allee effect. These behaviors can be interpreted on the basis of a biological model of population evolution.