Abstract In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii’s theory of periodic solution, we prove that the system admits a positive T-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability.

中文翻译：

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具有分布式延迟和一般功能响应的随机捕食者-猎物模型的动力学行为

摘要 在本文中，我们研究了两个具有分布式延迟和一般功能响应的随机捕食者-猎物模型。对于系统的非自治周期情况，利用Khasminskii的周期解理论，证明了系统存在正的T-周期解。对于同时受到白噪声和有色噪声扰动的系统，我们建立了系统解正递归存在的充分条件。正递归的存在意味着随机弱稳定性。