Based on the fact that the continuous culture of microorganisms in a chemostat is subject to environmental noises, we present and analyze a stochastic competition chemostat model with general monotonic response functions and differential removal rates. The existence and boundedness of the unique positive solution are first obtained. By defining a stochastic break-even concentration for every species, we prove that at most one competitor survives in the chemostat and the winner has the smallest stochastic break-even concentration, provided its response function satisfies a technical assumption. That is to say, the competitive exclusion principle holds for the stochastic competition chemostat model. Furthermore, we find that the noise experienced by one species is adverse to its growth while may be favorable for the growth of other one species. Namely, the destinies can be exchanged between two microorganism species in the chemostat due to the environmental noise.

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具有随机扰动的一般多物种恒化器模型中的竞争排除

基于恒化器中微生物的连续培养受环境噪声影响的事实，我们提出并分析了具有一般单调响应函数和差异去除率的随机竞争恒化器模型。首先得到唯一正解的存在性和有界性。通过为每个物种定义一个随机盈亏平衡浓度，我们证明了在恒化器中最多有一个竞争者幸存下来，而获胜者的随机盈亏平衡浓度最小，前提是其响应函数满足技术假设。也就是说，竞争排除原理适用于随机竞争恒化器模型。此外，我们发现一种物种所经历的噪音对其生长不利，而可能有利于另一种物种的生长。