In this paper, we propose and investigate a stochastic Holling type-II predator–prey model with prey refuge and fear effect. We first prove the existence and uniqueness of the global positive solution. Then we perform the survival analysis of the model, including the existence of a unique ergodic stationary distribution and the extinction of the model. Numerical simulations are carried out to validate our analytical results. Our findings indicate that the white noise is adverse to the growth of predator and prey populations, and the increase of fear effect will lead to the decrease of predator density, but with no obvious effect on prey density.

中文翻译：

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具有猎物避难所和恐惧效应的随机捕食者-猎物模型的生存分析

在本文中，我们提出并研究了具有猎物避难所和恐惧效应的随机 Holling II 型捕食者-猎物模型。我们首先证明全局正解的存在性和唯一性。然后我们对模型进行生存分析，包括存在唯一遍历平稳分布和模型的消亡。进行数值模拟以验证我们的分析结果。我们的研究结果表明，白噪声不利于捕食者和猎物种群的增长，恐惧效应的增加会导致捕食者密度的降低，但对猎物密度没有明显影响。