Complex Dynamics of a Stochastic Two-Patch Predator-Prey Population Model with Ratio-Dependent Functional Responses

This paper investigates a stochastic two-patch predator-prey model with ratio-dependent functional responses. First, the existence of a unique global positive solution is proved via the stochastic comparison theorem. Then, two different methods are used to discuss the long-time properties of the solutions pathwise. Next, sufficient conditions for extinction and persistence in mean are obtained. Moreover, stochastic persistence of the model is discussed. Furthermore, sufficient conditions for the existence of an ergodic stationary distribution are derived by a suitable Lyapunov function. Next, we apply the main results in some special models. Finally, some numerical simulations are introduced to support the main results obtained. The results in this paper generalize and improve the previous related results.

Automated summary

This paper proves the existence of a unique global positive solution in a stochastic two-patch predator-prey model with ratio-dependent functional responses through the stochastic comparison theorem. It discusses the long-time properties of the solutions pathwise using two different methods and obtains sufficient conditions for extinction and persistence in mean. The results also include discussions on stochastic persistence and the existence of an ergodic stationary distribution, with applications to special models and numerical simulations to support the main results.