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Global dynamics of the chemostat with different removal rates and variable yields

Tewfik Sari 1, 2 Frédéric Mazenc 3
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
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
Inria Saclay - Ile de France, L2S - Laboratoire des signaux et systèmes
Abstract : In this paper, we consider a competition model between n species in a chemostat including both monotone and non-monotone growth functions, distinct removal rates and variable yields. We show that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. We construct a Lyapunov function which reduces to the Lyapunov function used by S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growth functions are of Michaelis-Menten type and the yields are constant. Various applications are given including linear, quadratic and cubic yields.
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Submitted on : Tuesday, May 11, 2010 - 10:22:47 AM
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Tewfik Sari, Frédéric Mazenc. Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences and Engineering, AIMS Press, 2011, 8 (3), pp.827-840. ⟨10.3934/mbe.2011.8.827⟩. ⟨hal-00418676v2⟩

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