The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

中文翻译：

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具有S型分布时滞和Lévy跳的随机竞争模型的最优收获策略

本文的目的是通过遍历方法研究具有S型分布时滞和Lévy跳的随机竞争Lotka-Volterra模型的最优收获策略。首先，在一些适当的假设下，建立了每个物种灭绝的充分条件和在平均时间上稳定的条件。其次，在一个技术假设下，证明了该模型的分布稳定性。然后，在所有物种均具有持久性的条件下，为存在最优采伐政策建立了充分和必要的标准。此外，给出了最佳收获努力和最大可持续产量的明确表述。