Math. Model. Nat. Phenom.
Volume 13, Number 3, 2018
Modelling in Ecology, Epidemiology and Evolution
|Number of page(s)||21|
|Published online||06 September 2018|
Steady state analysis of a syntrophic model: the effect of a new input substrate concentration
Université de Tunis El Manar, École Nationale d’Ingénieurs de Tunis, LAMSIN, BP 37, Le Belvédère,
2 UMR Mistea, INRA, Université de Montpellier, 34060 Montpellier, France.
3 UMR Itap, Irstea, Université de Montpellier, 34196 Montpellier, France.
4 LBE, INRA, Université de Montpellier, 11100 Narbonne, France.
5 Université de Manouba, ENSI, Campus Universitaire de Manouba, 2010 Manouba, Tunisie.
6 Université de Haute Alsace, LMIA, 4 rue des frères Lumière, 68093 Mulhouse, France.
* Corresponding author: email@example.com
Accepted: 9 March 2018
In this work, we are interested in a reduced and simplified model of the anaerobic digestion process. We focus on the acetogenesis and hydrogenetrophic methanogenesis phases. The model describes a syntrophic relashionship between two microbial species (the acetogenic bacteria and the hydrogenetrophic methanogenic bacteria) with two input substrates (the fatty acids and the hydrogen) including both decay terms and inhibition of the acetogenic bacteria growth by an excess of hydrogen in the system. The existence and stability analysis of the steady states of the model points out the existence of a new equilibrium point which can be stable according to the operating parameters of the system. By means of operating diagrams, we show that, whatever the region of space considered, there exists only one locally exponentially stable steady state.
Mathematics Subject Classification: 34D20 / 92D25 / 92C45
Key words: Microbial ecosystems / syntrophic relationship / mortality / stability / operating diagrams
© EDP Sciences, 2018
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