In this paper, we study the dynamics of stochastic time-delayed predator–prey model with modified Leslie–Gower and ratio-dependent schemes including additional food for predator and prey with Michaelis–Menten type harvest. We introduce the effects of time delay, Michaelis–Menten type harvest and stochastic perturbation under the structure of the original model to make the model more consistent with the actual system. We first prove that the system has a globally unique positive solution. Secondly we obtain conditions for the persistence in mean and extinction of the system. Besides, we verify that the system is stochastic permanence under certain conditions. In addition to that, we prove that the system has an ergodic stationary distribution when the parameters satisfy certain conditions. Finally, some numerical simulations were performed to verify the correctness and validity of the theoretical results.

在本文中，我们研究了随机延迟捕食者 - 猎物模型的动力学，该模型具有改进的 Leslie-Gower 和比率相关方案，包括使用 Michaelis-Menten 类型收获为捕食者和猎物提供额外食物。我们在原始模型的结构下引入了时间延迟、Michaelis-Menten 型收获和随机扰动的影响，使模型与实际系统更加一致。我们首先证明该系统具有全局唯一的正解。其次，我们获得了系统的均值持久性和灭绝性的条件。此外，我们验证了系统在一定条件下是随机的。除此之外，我们证明了当参数满足一定条件时，系统具有遍历平稳分布。最后，