Analysis of a stochastic population model with mean-reverting Ornstein–Uhlenbeck process and Allee effects

Abstract

Considering the survival regulation mechanisms of many groups of animals and the complexity of random variations in ecosystem, in this paper, we mainly formulate and study a stochastic non-autonomous population model with Allee effects and two mean-reverting Ornstein–Uhlenbeck processes. First, the biological implication of introducing the Ornstein–Uhlenbeck process is illustrated. After that, we give the existence and moment estimate of a global solution of the stochastic model. Then the sufficient criteria for exponential extinction and the existence of a stationary distribution of the stochastic model are established. Moreover, there are some challenges to give the explicit expression of probability density function of the stationary distribution. By solving the relevant Fokker–Planck equation, we derive the approximate expression of the density function of the stochastic model. Finally, some numerical simulations are provided to verify our analytical results and study the impact of stochastic noises on population dynamics.