A Lyapunov function for the chemostat with variable yields

Tewfik Sari

doi:10.1016/j.crma.2010.06.008

Ordinary Differential Equations

A Lyapunov function for the chemostat with variable yields
[Une fonction de Lyapunov pour le chemostat avec des rendements variables]

Présenté par : Pierre-Louis Lions

Tewfik Sari ^1,²

¹ EPI MERE INRIA-INRA, UMR MISTEA, 2, place Viala, 34060 Montpellier, France
² Laboratoire de mathématiques, informatique et applications, université de Haute Alsace, 4, rue des frères Lumière, 68093 Mulhouse, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 747-751.

Résumé
Abstract

Dans cette Note on propose une nouvelle fonction de Lyapunov pour l'étude de la stabilité asymptotique globale dans un modèle mathématique de compétition entre esspèces dans le chemostat. Le modèle inclut des fonctions de croissance monotones ou non monotones, des taux de mortalité différents pour chaque espèce et des taux de rendement variables, fonctions de la concentration en substrat. On obtient, comme corollaires de notre résultat, trois théorèmes de stabilité globale qui ont été considérés dans la litérature.

In this Note, we give a global asymptotic stability result for the competition mathematical model between several species in a chemostat, by using a new Lyapunov function. The model includes both monotone and non-monotone response functions, distinct removal rates for the species and variable yields, depending on the concentration of substrate. We obtain, as corollaries of our result, three global stability theorems which were considered in the literature.

Reçu le : 2010-03-01
Accepté le : 2010-06-03
Publié le : 2010-06-23

DOI : 10.1016/j.crma.2010.06.008

Affiliations des auteurs :

Tewfik Sari ^{1, 2}

¹ EPI MERE INRIA-INRA, UMR MISTEA, 2, place Viala, 34060 Montpellier, France
² Laboratoire de mathématiques, informatique et applications, université de Haute Alsace, 4, rue des frères Lumière, 68093 Mulhouse, France

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     title = {A {Lyapunov} function for the chemostat with variable yields},
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     year = {2010},
     doi = {10.1016/j.crma.2010.06.008},
     language = {en},
}

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Tewfik Sari. A Lyapunov function for the chemostat with variable yields. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 747-751. doi : 10.1016/j.crma.2010.06.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.008/

Bibliographie
Cité par

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