Extensions of the chemostat model with flocculation

Radhouane Fekih-Salem (1, 2) , Alain Rapaport (1, 2) , Tewfik Sari (1, 2, 3) , Claude Lobry (1) , Jérôme Harmand (1, 4)

1 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
4 LBE - Laboratoire de Biotechnologie de l'Environnement [Narbonne]

In this work, we study a model of the chemostat where the species are present in two forms, isolated bacteria and under an aggregated form like attached bacteria or bacteria in flocks. We show that our general model contains a lot of models which were previously considered in the literature. Assuming that flocculation and deflocculation dynamics are fast with respect to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bistability, while it may only occur in the classical chemostat model when the growth rate in non monotonic.

Mots clés: Chemostat; density dependent growth functions; flocculation

Domaines: Systèmes dynamiques [math.DS]

Radhouane Fekih-Salem, Alain Rapaport, Tewfik Sari, Claude Lobry, Jérôme Harmand. Extensions of the chemostat model with flocculation. 2011. ⟨hal-00604633v2⟩