Analysis of a stochastic two-species predator-prey system in two-patch environments with Ornstein-Uhlenbeck process

To characterize the effects of diffusion and environmental noise on population dynamics, in the paper, we first develop a stochastic two-species predator-prey model in two-patch environments, where the fluctuations in the environment are depicted by an Ornstein-Uhlenbeck process. Then we analyze the dynamical behavior of the stochastic model in detail, including the existence and uniqueness of the global solution, the pth moment boundedness, asymptotic pathwise estimation and the existence of a stationary distribution. It is worth noting that by solving the six-dimensional algebraic equations corresponding to the stochastic model, we get the approximate expression of the probability density function around the quasi-coexistence equilibrium of the stochastic system. Finally, a series of numerical simulations are presented to confirm the feasibility and correctness of our theoretical analysis results. Our findings show the importance of considering the effect of this type of stochastic process on the population dynamics.