We consider the feedback control for a model of competition in a chemostat with one single substrate and two species. De Leenheer and Smith [J.Math.Biol.,46 (2003), pp.48-70] studied the competition in the chemostat in the framework of feedback control theory, giving sufficient conditions for the convergence of the species toward a unique stable critical point, thus avoiding the competitive exclusion. Nevertheless, they suppose that the mortality rates can be neglected. In this paper we allow non-zero mortality rates and the results stated before can be extended: We also obtain sufficient conditions (summarized as upper bounds for the size of mortality rates) for the convergence of competing species toward a unique stable critical point.
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机译：我们考虑在具有一个单一底物和两个物种的化学恒温器中的竞争模型的反馈控制。 De Leenheer和Smith [J.Math.Biol。，46（2003），pp.48-70]在反馈控制理论的框架内研究了恒化器中的竞争，为物种趋向唯一稳定化提供了充分的条件。临界点，从而避免竞争排斥。然而，他们认为死亡率可以忽略。在本文中，我们允许非零死亡率，并且可以扩展之前所述的结果：我们还获得了充足的条件（概括为死亡率的上限），以使竞争物种趋向唯一稳定的临界点。
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