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

Tewfik Sari (1, 2) , Frédéric Mazenc (3)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
2 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

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.

Mots clés: Chemostat; Competitive exclusion principle; Lyapunov function; Global asymptotic stability; Variable yield model

Domaines: Systèmes dynamiques [math.DS]

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⟩