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[J]. Mathematical Biosciences and Engineering, 2012, 9(3): 627-645. doi: 10.3934/mbe.2012.9.627
Abstract
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.