American Institute of Mathematical Sciences

Advanced
2008, 5(3): 539-547. doi: 10.3934/mbe.2008.5.539

Biological control of the chemostat with nonmonotonic response and different removal rates

Alain Rapaport 1, and  Jérôme Harmand 2,

1. 

UMR Analyse des Systèmes et Biométrie, INRA, EPI INRA/INRIA 'MODEMIC', 2 pl. Viala 34060 Montpellier, France
2. 

Laboratoire de Biotechnologie de l'Environnement, INRA, Avenue des Etangs, 11100 Narbonne, France

Received  October 2007 Revised  April 2008 Published  June 2008

We show the global stabilization of the chemostat with nonmonotonic growth, adding a new species as a ''biological'' control, in presence of different removal rates for each species. This result is obtained by an extension of the Competitive Exclusion Principle in the chemostat, for the case of two species with different removal rates and at least one nonmonotonic response.
Keywords: global stabilization., competition exclusion, chemostat.
Mathematics Subject Classification: Primary: 34D05, 34D23, 92D25; Secondary: 93C1.
Citation: Alain Rapaport, Jérôme Harmand. Biological control of the chemostat with nonmonotonic response and different removal rates. Mathematical Biosciences & Engineering, 2008, 5 (3) : 539-547. doi: 10.3934/mbe.2008.5.539
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