A stochastic four species food-chain model is proposed in this paper. Here, artificial harvest in each species and the effect of time delay for interaction between species are considered, which makes the model more applicable in real situations. Specifically, we address the stochastic global dynamics behavior, including the existence of global positive solutions, stochastic ultimate boundedness, extinction with probability one, persistence in mean and global stability. The asymptotic stability in the probability distribution is obtained, and the criterion for the existence and non-existence of the optimal harvesting strategy is also derived. Furthermore, this paper can provide reference for the research of general n-species stochastic food-chain models.

中文翻译：

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具有收获和分布时滞的随机四种群食物链模型的动态分析

提出了一种随机的四物种食物链模型。在这里，考虑了每个物种的人工收获以及物种之间相互作用的时间延迟的影响，这使得该模型更适用于实际情况。具体来说，我们解决了随机的全局动力学行为，包括全局正解的存在，随机的最终有界性，以概率1灭绝，均值的持续性和全局稳定性。获得了概率分布的渐近稳定性，并推导了最优收获策略存在与否的判据。此外，本文还可以为研究一般的n种随机食物链模型提供参考。