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

Miled El Hajji; Frédéric Mazenc; Jérôme Harmand; Miled El Hajji; Frédéric Mazenc; Jérôme Harmand

doi:10.3934/mbe.2010.7.641

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 3: 641-656. doi: 10.3934/mbe.2010.7.641

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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
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

Received: 01 October 2009 Accepted: 29 June 2018 Published: 01 June 2010
MSC : Primary: 92B05, 92D25; Secondary: 34A34, 34D23.

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.
- Syntrophic relationship,
- Mathematical modelling,
- Anaerobic digestion,
- Coexistence.,
- Asymptotic stability
Citation: Miled El Hajji, Frédéric Mazenc, Jérôme Harmand. A mathematical study of a syntrophic relationship of a modelof anaerobic digestion process[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 641-656. doi: 10.3934/mbe.2010.7.641

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Abstract

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.
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