# American Institute of Mathematical Sciences

2012, 9(3): 627-645. doi: 10.3934/mbe.2012.9.627

## The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat

 1 Irstea, UMR ITAP, 361 rue Jean-François Breton 34196 Montpellier, & Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 Montpellier, France 2 ISSATSO (Université de Sousse) Cité Taffala, 4003 Sousse, & LAMSIN-ENIT, Université Tunis El-manar BP 37, 1002 Tunis, Tunisia 3 INRA UR0050, Laboratoire de Biotechnologie de l’Environnement, Avenue des Étangs, 11100 Narbonne, and Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 Montpellier, France

Received  November 2011 Revised  April 2012 Published  July 2012

A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out as well as the analysis of the local and global stability of the equilibria. We demonstrate, under general assumptions of monotonicity which are relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.
Citation: Tewfik Sari, Miled El Hajji, Jérôme Harmand. The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat. Mathematical Biosciences & Engineering, 2012, 9 (3) : 627-645. doi: 10.3934/mbe.2012.9.627
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