A stochastic Holling-type II predator-prey model with stage structure and refuge for prey
In this paper, a stochastic Holling-type II predator-prey model with stage structure and refuge for prey is analyzed. Firstly, the existence and uniqueness of the global positive solution for this predator-prey model have been proved. Due to its nonexplosive property, the authors obtain the conditions for the stochastically ultimate boundedness of positive solution. Next, the sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solution are established. Then, the authors obtain sufficient conditions for the extinction of predator population in two cases and that of prey population in one case. The theoretical results are proved by numerical simulations. The main reference is the work of \textit{A. Das} and \textit{G. P. Samanta} [``A prey-predator model with refuge for prey and additional food for predator in a fluctuating environment'', Phys. A: Stat. Mech. Appl. 538, Article ID 122844 (2019; \url{doi:10.1016/j.physa.2019.122844})].
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