Due to the complex set of abiotic and biotic interaction variables in the ecosystems, the dynamics of animal populations are generally considered to be driven in astate-dependent manner. This paper presents an analysis of a stochastic Nicholson's blowflies model with distributed delay, which consists of the existence and uniqueness of globally positive solution, extinction, existence of positive T-periodic solution and positive recurrence. Our results suggest that a smaller white noise is necessary to cause the existence of positive T-periodic solution and positive recurrence of the stochastic model, while a larger white noise will accelerate the extinction of the population. In addition, numerical simulation is used to support our main results.

中文翻译：

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具有分布式延迟的随机 Nicholson's 苍蝇模型的平稳分布和周期解

由于生态系统中一组复杂的非生物和生物相互作用变量，动物种群的动态通常被认为是以状态依赖的方式驱动的。本文分析了具有分布式延迟的随机 Nicholson's Blowflies 模型，该模型由全局正解的存在性和唯一性、灭绝性、正T周期解的存在性和正递归性组成。我们的结果表明，需要较小的白噪声才能导致正T-周期解的存在和随机模型的正递归，而较大的白噪声会加速种群的灭绝。此外，数值模拟用于支持我们的主要结果。