A density-dependent model of competition for one resource in the chemostat

Radhouane Fekih-Salem (1, 2) , Claude Lobry (3) , Tewfik Sari (4, 5)

1 UM - Université de Monastir - University of Monastir
2 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
3 UNS - Université Nice Sophia Antipolis (1965 - 2019)
4 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
5 UMR ITAP - Information – Technologies – Analyse Environnementale – Procédés Agricoles

This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra-and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra-and interspecific competition, this general model is first studied by determining the conditions of existence and local stability of steady states. With the same removal rate, the model can be reduced to a planar system and then the global stability results for each steady state are derived. The bifurcations of steady states according to interspecific competition parameters are analyzed in a particular case of density-dependent growth rates which are usually used in the literature. The operating diagrams show how the model behaves by varying the operating parameters and illustrate the effect of the intra-and interspecific competition on the disappearance of coexistence region and the occurrence of bi-stability region. Concerning the small enough interspecific competition terms, we would shed light on the global convergence towards the coexistence steady state for any positive initial condition. And, as far as the large enough interspecific competition terms, this system exhibits bi-stability with competitive exclusion of one species according to the initial condition.

Mots clés: Bifurcation; Chemostat; Coexistence; Competition; Density-dependence; Global stability

Domaines: Systèmes dynamiques [math.DS]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]; Statistiques [math.ST]

Radhouane Fekih-Salem, Claude Lobry, Tewfik Sari. A density-dependent model of competition for one resource in the chemostat. Mathematical Biosciences, In press, 286, pp.104-122. ⟨10.1016/j.mbs.2017.02.007⟩. ⟨hal-01359078⟩