title: A density-dependent model of competition for one resource in the chemostat.
abstract: 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 interference, 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 interference 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 interference on the disappearance of coexistence region and the occurrence of bi-stability region. Concerning the small enough interspecific interference terms, we would shed light on the global convergence towards the coexistence steady state for any positive initial condition. When the interspecific interference pressure is large enough this system exhibits bi-stability where the issue of the competition depends on the initial condition.
authors.affiliation: Université de Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 Tunis, Tunisie; Université de Monastir, ISIMa, BP 49, Av Habib Bourguiba, 5111 Mahdia, Tunisie. Electronic address: radhouene.fekihsalem@isima.rnu.tn.
authors.forename: Radhouane
authors.initials: R
authors.lastname: Fekih-Salem
authors.affiliation: Université de Nice et MODEMIC, Le Gd Palais Bt6, 2 BD de Cimiez, 06000 Nice, France. Electronic address: lobrinria@wanadoo.fr.
authors.forename: Claude
authors.initials: C
authors.lastname: Lobry
authors.affiliation: IRSTEA, UMR Itap, 361 rue Jean-François Breton, 34196 Montpellier, France; Université de Haute Alsace, LMIA, 4 rue des frères Lumière, 68093 Mulhouse, France. Electronic address: tewfik.sari@irstea.fr.
authors.forename: Tewfik
authors.initials: T
authors.lastname: Sari
mesh_terms: D017753:Ecosystem; D056265:Microbial Interactions; D008954:Models, Biological
keywords: Bifurcation; Chemostat; Coexistence; Competition; Density-dependence; Global stability