具有Holling Ⅲ功能性反应的随机捕食食饵模型的平稳分布和周期解

Abstract

Abstract:

In this paper, we investigate the dynamics of stochastic predator-prey systems with Holling-type Ⅲ functional response. For the autonomous system, we firstly obtain that the system admits unique positive global solution starting from the positive initial value. Then, by comparison theorem for stochastic differential equation, sufficient conditions for extinction and persistence in mean are obtained. Thirdly, by constructing some suitable Lyapunov function, we prove that there are unique stationary distribution and they are ergodic. On the other hand, for the non-autonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Has'minskii. Finally, some numerical simulations are introduced to illustrate our theoretical result.

Key words: Predator-prey system, Random perturbation, Stationary distribution and ergodicity, Periodic solution

CLC Number:

O211.63

Guijie Lan,Yingjie Fu,Chunjin Wei,Shuwen Zhang. Stationary Distribution and Periodic Solution for Stochastic Predator-Prey Systems with Holling-Type Ⅲ Functional Response[J].Acta mathematica scientia,Series A, 2018, 38(5): 984-1000.

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References 18

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Stationary Distribution and Periodic Solution for Stochastic Predator-Prey Systems with Holling-Type Ⅲ Functional Response

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