A stochastic two-prey one-predator system with distributed delays is proposed in this paper. Firstly, applying the linear chain technique, we transform the predator–prey system with distributed delays to an equivalent system with no delays. Then, by use of the comparison method and the inequality technique, we investigate the stability in mean and extinction of species. Further, by constructing some suitable functionals, using M-matrix theory and three important lemmas, we establish sufficient conditions assuring the existence of distribution and the attractivity of solutions. Finally, some numerical simulations are given to illustrate the main results.

中文翻译：

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具有分布式延迟的随机三物种捕食者-猎物系统的动力学分析

本文提出了一种具有分布式时延的随机二食一食者系统。首先，应用线性链技术，我们将具有分布式延迟的捕食者-猎物系统转换为没有延迟的等效系统。然后，通过比较方法和不等式技术，我们研究了物种均值和灭绝的稳定性。此外，通过构造一些合适的泛函，使用 M 矩阵理论和三个重要的引理，我们建立了保证分布存在和解的吸引力的充分条件。最后，给出了一些数值模拟来说明主要结果。