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Article Dans Une Revue Mathematical Biosciences and Engineering Année : 2011

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

Résumé

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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Dates et versions

hal-00418676 , version 1 (21-09-2009)
hal-00418676 , version 2 (11-05-2010)

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Citer

Tewfik Sari, Frédéric Mazenc. Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences and Engineering, 2011, 8 (3), pp.827-840. ⟨10.3934/mbe.2011.8.827⟩. ⟨hal-00418676v2⟩
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