Abstract

Stochastic differential models provide an additional degree of realism compared to their corresponding deterministic counterparts because of the randomness and stochasticity of real life. In this work, we study the dynamics of a stochastic delay differential model for prey–predator system with hunting cooperation in predators. Existence and uniqueness of global positive solution and stochastically ultimate boundedness are investigated. Some sufficient conditions for persistence and extinction, using Lyapunov functional, are obtained. Illustrative examples and numerical simulations, using Milstein’s scheme, are carried out to validate our analytical findings. It is observed that a small scale of white noise can promote the survival of both species; while large noises can lead to extinction of the predator population.

中文翻译：

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食饵具有捕食合作的捕食系统的随机时滞差分模型的持续灭绝。

摘要

由于其随机性和随机性，随机微分模型与其对应的确定性模型相比，提供了更高的真实性。在这项工作中，我们研究了具有捕食合作关系的食饵-捕食者系统的随机时滞差分模型的动力学。研究了整体正解的存在唯一性和随机极限界。使用Lyapunov函数，获得了一些足以持久和灭绝的条件。使用Milstein的方案进行了说明性示例和数值模拟，以验证我们的分析结果。据观察，小规模的白噪声可以促进两个物种的生存。而较大的噪音可能导致捕食者灭绝。