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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 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
  • Received: 01 April 2010 Accepted: 29 June 2018 Published: 01 June 2011

  • MSC : Primary: 92A15, 92A17; Secondary: 34C15, 34C35.

  • 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.

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

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  • 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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    4. Guihong Fan, Hal L. Smith, Horst R. Thieme, Competition in the Chemostat with Time-Dependent Differential Removal Rates, 2017, 45, 2305-221X, 153, 10.1007/s10013-016-0208-9
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  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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