This paper is concerned with a stochastic predator–prey model with Holling II increasing function in the predator. By applying the Lyapunov analysis method, we demonstrate the existence and uniqueness of the global positive solution. Then we show there is a stationary distribution which implies the stochastic persistence of the predator and prey in the model. Moreover, we obtain respectively sufficient conditions for weak persistence in the mean and extinction of the prey and extinction of the predator. Finally, some numerical simulations are given to illustrate our main results and the discussion and conclusion are presented.

中文翻译：

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捕食者中具有 Holling II 递增函数的捕食者-猎物随机模型

本文关注的是一个随机捕食者 - 猎物模型，在捕食者中具有 Holling II 递增函数。通过应用李雅普诺夫分析方法，我们证明了全局正解的存在性和唯一性。然后我们展示了一个平稳分布，这意味着模型中捕食者和猎物的随机持久性。此外，我们分别获得了猎物的平均和灭绝和捕食者的灭绝的弱持久性的充分条件。最后，给出了一些数值模拟来说明我们的主要结果，并给出了讨论和结论。