Analysis of a stochastic food chain model with nonlinear prey refuge and Allee effect driven by Ornstein-Uhlenbeck process

In this paper, we investigated a food chain model driven by the Ornstein-Uhlenbeck process, incorporating the Holling type Ⅱ functional response, nonlinear prey refuge, and the Allee effect in the top predator. First, the biological significance of the Ornstein-Uhlenbeck process was illustrated, and its rationality was explained. Subsequently, the existence and uniqueness of the global solution of the model were established, and its ultimate boundedness was analyzed. Then, by constructing a Lyapunov function and applying Itô's formula, the existence of the stationary distribution of the model was demonstrated. Furthermore, the conditions for the system extinction were provided. Finally, numerical simulations were conducted to verify the theoretical results and confirm the validity of the conclusions.