In this paper, a model of stochastic competition between plasmid-bearing and plasmid-free organisms in a chemostat is investigated. First, we show that there is a unique global positive solution for the stochastic system. Second, by employing stochastic Lyapunov functions, Itô formula, strong law of large number and some other important inequalities, stochastic characteristics of the stochastic competition chemostat model are studied such as the stochastic asymptotic behaviors of the system. Finally, some numerical simulations are given.

中文翻译：

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恒化器模型中含质粒和不含质粒的生物体之间随机竞争的动态行为

在本文中，研究了恒化器中携带质粒和无质粒生物之间的随机竞争模型。首先，我们证明了随机系统有一个独特的全局正解。其次，利用随机Lyapunov函数、Itô公式、强大数定律等重要不等式，研究了随机竞争恒化器模型的随机特性，如系统的随机渐近行为。最后给出了一些数值模拟。