Feedback control for competition models with different removal rates in the chemostat
Abstract
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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