A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey

Abstract

In this paper, we study a stochastic Holling-type II predator-prey model with stage structure and refuge for prey. Firstly, the existence and uniqueness of the global positive solution of the system are proved. Secondly, the stochastically ultimate boundedness of the solution is discussed. Next, sufficient conditions for the existence and uniqueness of ergodic stationary distribution of the positive solution are established by constructing a suitable stochastic Lyapunov function. Then, sufficient conditions for the extinction of predator population in two cases and that of prey population in one case are obtained. Finally, some numerical simulations are presented to verify our results.

Extinction and strong persistence in the Beddington–DeAngelis predator–prey random model

“…From biological and mathematical points of view, the stochastic predator–prey model can predict future dynamics more accurately than the deterministic model. For instance, Shi et al [6] considered a stochastic Holling‐Type II predator–prey model with stage structure and refuge for prey; Zhang et al [7] studied the dynamic of a stochastic Holling III predator–prey system with a prey refuge; Roy et al [8] established a predator–prey system with a fear factor in a stochastic environment. Rihan and Alsakaji [9] considered the dynamics of a stochastic delay prey–predator system with untiring cooperation in predators; Alsakaji et al [10] studied the dynamics of a delay differential model of predator–prey system with Monod–Haldane and Holling type II functional responses.…”