Global dynamics of the buffered chemostat for a general class of response functions

Alain Rapaport (1, 2) , Ihab Haidar (3, 4) , Jérôme Harmand (1, 5)

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 GECO - Geometric Control Design
4 L2S - Laboratoire des signaux et systèmes
5 LBE - Laboratoire de Biotechnologie de l'Environnement [Narbonne]

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to setup or on the opposite to go to extinction, depending on the characteristics of the buffer. For non-monotonic response function, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function.

Mots clés: interconnection; chemostat; multi-stability; global asymptotic stability

Domaines: Systèmes dynamiques [math.DS]; Ecosystèmes

Alain Rapaport, Ihab Haidar, Jérôme Harmand. Global dynamics of the buffered chemostat for a general class of response functions. Journal of Mathematical Biology, 2015, 71 (1), pp.69-98. ⟨10.1007/s00285-014-0814-7⟩. ⟨hal-00923826⟩