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Competitive Exclusion for Chemostat Equations with Variable Yields

Tewfik Sari 1, 2
2 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
CRISAM - Inria Sophia Antipolis - Méditerranée , MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
Abstract : In this paper, we study the global dynamics of a chemostat model with a single nutrient and several competing species. Growth rates are not required to be proportional to food uptakes. Our approach is based on the construction of Lyapunov functions. The Lyapunov functions extend those used by Hsu (SIAM J. Appl. Math. 34:760-763, 1978) and by Wolkowicz and Lu (SIAM J. Appl. Math. 52:222-233, 1992) in the case when growth rates are proportional to food uptakes. Our result generalizes a large variety of previous results obtained by Lyapunov techniques.
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Tewfik Sari. Competitive Exclusion for Chemostat Equations with Variable Yields. Acta Applicandae Mathematicae, Springer Verlag, 2012, 123 (1), p. 201 - p. 219. ⟨10.1007/s10440-012-9761-8⟩. ⟨hal-00780065⟩

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