Dynamics of a stochastic single species model with mean-reverting Ornstein-Uhlenbeck and Allee effect

This paper studies the dynamics of a stochastic single species model with Ornstein-Uhlenbeck process and Allee effect. First, we establish the existence of a unique global solution and obtain moment estimates. Then, sufficient conditions for the existence of a unique stationary distribution of the model and for the extinction of species are derived. The results show that a weaker attack rate guarantees a unique stationary distribution, whereas a stronger attack rate leads to species extinction. Moreover, we obtain an approximate expression for the stationary density around the stochastic quasi-positive equilibrium by solving the associated Fokker-Planck equation. Finally, some numerical simulations are presented.