In this paper, the stochastic dynamics of a hybrid delay food chain model with harvesting and Lévy jumps in a polluted environment is studied by using stochastic analysis techniques. Under some basic assumptions, criterions about stochastic persistence in mean and extinction of each species are established, as well as global attractivity and the existence of optimal harvesting strategy (OHS) of the system. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the stochastic dynamics and OHS of the system are closely correlated with both time delays and environmental noises. Finally, some numerical simulations are introduced to illustrate the main results.

本文利用随机分析技术研究了污染环境中具有收获和 Lévy 跳跃的混合延迟食物链模型的随机动力学。在一些基本假设下，建立了关于每个物种的平均和灭绝的随机持续性的标准，以及系统的全局吸引力和最优收获策略（OHS）的存在性。给出了最佳收获努力（OHE）和最大可持续产量期望（MESY）的准确表达式。我们的结果表明，系统的随机动力学和 OHS 与时间延迟和环境噪声密切相关。最后，介绍了一些数值模拟来说明主要结果。