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

Jean-Luc Gouzé 1 Gonzalo Robledo 1
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
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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Submitted on : Friday, May 19, 2006 - 8:31:47 PM
Last modification on : Tuesday, December 8, 2020 - 3:35:44 AM
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  • HAL Id : inria-00070451, version 1

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Jean-Luc Gouzé, Gonzalo Robledo. Feedback control for competition models with different removal rates in the chemostat. [Research Report] RR-5555, INRIA. 2006, pp.26. ⟨inria-00070451⟩

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