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

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  • Wanying Shi
  • Youlin Huang
  • Chunjin Wei
  • Shuwen Zhang

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.

Suggested Citation

  • Wanying Shi & Youlin Huang & Chunjin Wei & Shuwen Zhang, 2021. "A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-14, July.
    • Handle: RePEc:hin:jnlamp:9479012
    DOI: 10.1155/2021/9479012
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