Mathematical Biosciences and Engineering, 2011, 8(3): 827-840. doi: 10.3934/mbe.2011.8.827.

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

1. Université de Haute Alsace, Mulhouse
2. Projet INRIA DISCO, CNRS-SUPELEC, 3 Rue Joliot Curie, 91192, Gif-sur-Yvette

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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Keywords Lyapunov function; competitive exclusion principle; Chemostat; global asymptotic stability; variable yield model.

Citation: Tewfik Sari, Frederic Mazenc. Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences and Engineering, 2011, 8(3): 827-840. doi: 10.3934/mbe.2011.8.827

 

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