In this paper, stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are considered. We first show the existence of the global positive solution, then discuss the effects of noises on the extinction of the species and the stochastic persistence of the species. In the meanwhile, numerical simulations are carried to support results. Finally, we show the existence of the stationary distribution for a special case.

中文翻译：

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具有 Beddington-DeAngelis 函数响应的二消费者一资源竞争系统的随机动力学分析

在本文中，考虑了具有 Beddington-DeAngelis 函数响应的二消费者一资源竞争系统的 Lévy 噪声随机动力学。我们首先证明了全局正解的存在，然后讨论了噪声对物种灭绝和物种随机持续性的影响。同时，进行数值模拟以支持结果。最后，我们展示了特殊情况下平稳分布的存在。