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

  • 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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