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

Wanying Shi | Zendy; Youlin Huang | Zendy; Chunjin Wei | Zendy; Shuwen Zhang | Zendy

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

Author(s) -

Wanying Shi,

Youlin Huang,

Chunjin Wei,

Shuwen Zhang

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/9479012

Subject(s) - uniqueness , mathematics , lyapunov function , ergodic theory , predation , extinction (optical mineralogy) , population , functional response , type (biology) , predator , stationary distribution , control theory (sociology) , mathematical optimization , mathematical analysis , ecology , nonlinear system , statistics , computer science , markov chain , biology , paleontology , physics , demography , control (management) , quantum mechanics , artificial intelligence , sociology

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.

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