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Association between competition and obligate mutualism in a chemostat

Miled El Hajji 1, 2, 3 Jérôme Harmand 4 Hédia Chaker Claude Lobry 2
1 ASB - Analyse des Systèmes et Biométrie
2 MERE - Water Resource Modeling
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique : UMR0729
3 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
4 LBE - Laboratoire de Biotechnologie de l'Environnement [Narbonne]
Abstract : In this paper, we consider a simple chemostat model involving two obligate mutualistic species feeding on a limiting substrate. Systems of differential equations are proposed as models of this association. A detailed qualitative analysis is carried out. We show the existence of a domain of coexistence, which is a set of initial conditions in which both species survive. We demonstrate, under certain supplementary assumptions, the uniqueness of the stable equilibrium point which corresponds to the coexistence of the two species.
Keywords : MICROBIAL INTERACTIONS MICROBIAL ECOLOGY YEAST SACCHAROMYCES CEREVISIAE CHEMOSTAT COMPETITION MUTUALISM ASYMPTOTIC BEHAVIOUR COEXISTENCE DULAC CRITERION THIEME'S RESULT INTERACTION MICROBIOLOGIQUE
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https://hal.inria.fr/hal-00858541
Contributor : Alain Rapaport <>
Submitted on : Thursday, September 5, 2013 - 3:36:25 PM
Last modification on : Wednesday, February 10, 2021 - 3:35:52 AM

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Miled El Hajji, Jérôme Harmand, Hédia Chaker, Claude Lobry. Association between competition and obligate mutualism in a chemostat. Journal of Biological Dynamics, Taylor & Francis Open, 2009, 3 (6), pp.635 - 647. ⟨10.1080/17513750902915978⟩. ⟨hal-00858541⟩

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