Analysis of a stochastic fear effect predator-prey system with Crowley-Martin functional response and the Ornstein-Uhlenbeck process

This paper studied a stochastic fear effect predator-prey model with Crowley-Martin functional response and the Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process was illustrated. Subsequently, the existence and uniqueness of the global solution were then established. Moreover, the ultimate boundedness of the model was analyzed. Then, by constructing the Lyapunov function and applying $It\hat{o}$'s formula, the existence of the stationary distribution of the model was demonstrated. In addition, sufficient conditions for species extinction were provided. Finally, numerical simulations were performed to demonstrate the analytical results.