# American Institute of Mathematical Sciences

2010, 7(3): 641-656. doi: 10.3934/mbe.2010.7.641

## A mathematical study of a syntrophic relationship of a model of anaerobic digestion process

 1 UMR Analyses des Systèmes et Biométrie, INRA 02 Place, INRA-INRIA MERE research team, Viala, 34060 Montpellier, France, France 2 LBE-INRA, UR050, Avenue des Étangs, 11100 Narbonne & INRA-INRIA MERE research team, UMR Analyses des Systèmes et Biométrie, INRA 02 Place Viala, 34060 Montpellier, France

Received  October 2009 Revised  March 2010 Published  June 2010

A mathematical model involving the syntrophic relationship of two major populations of bacteria (acetogens and methanogens), each responsible for a stage of the methane fermentation process is proposed. A detailed qualitative analysis is carried out. The local and global stability analyses of the equilibria are performed. We demonstrate, under general assumptions of monotonicity, relevant from an applied point of view, the global asymptotic stability of a positive equilibrium point which corresponds to the coexistence of acetogenic and methanogenic bacteria.
Citation: Miled El Hajji, Frédéric Mazenc, Jérôme Harmand. A mathematical study of a syntrophic relationship of a model of anaerobic digestion process. Mathematical Biosciences & Engineering, 2010, 7 (3) : 641-656. doi: 10.3934/mbe.2010.7.641
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