Competition for a single resource and coexistence of several species in the chemostat

Nahla  Abdellatif; Radhouane  Fekih-Salem; Tewfik  Sari; Nahla  Abdellatif; Radhouane  Fekih-Salem; Tewfik  Sari

doi:10.3934/mbe.2016012

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 4: 631-652. doi: 10.3934/mbe.2016012

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Competition for a single resource and coexistence of several species in the chemostat

1.
Université de Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 Tunis
2.
IRSTEA, UMR Itap, 361 rue Jean-François Breton, 34196 Montpellier, France, and Université de Haute Alsace, LMIA, 4 rue des frères Lumière, 68093 Mulhouse

Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 May 2016
MSC : 92D25, 34D20, 34D43.

We study a model of the chemostat with several species in competition for a single resource.We take into account the intra-specific interactions between individuals of the same population of micro-organisms andwe assume that the growth rates are increasing and the dilution rates are distinct.Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria.Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium.Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species.The operating diagram describes the asymptotic behavior of this model with respect to control parametersand illustrates the effect of the intra-specific competition on the coexistence region of the species.
- coexistence,
- intra-specific,
- competition,
- Chemostat,
- operating diagram.
Citation: Nahla Abdellatif, Radhouane Fekih-Salem, Tewfik Sari. Competition for a single resource and coexistence of several species in the chemostat[J]. Mathematical Biosciences and Engineering, 2016, 13(4): 631-652. doi: 10.3934/mbe.2016012

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Abstract

We study a model of the chemostat with several species in competition for a single resource.We take into account the intra-specific interactions between individuals of the same population of micro-organisms andwe assume that the growth rates are increasing and the dilution rates are distinct.Using the concept of steady-state characteristics, we present a geometric characterization of the existence and stability of all equilibria.Moreover, we provide necessary and sufficient conditions on the control parameters of the system to have a positive equilibrium.Using a Lyapunov function, we give a global asymptotic stability result for the competition model of several species.The operating diagram describes the asymptotic behavior of this model with respect to control parametersand illustrates the effect of the intra-specific competition on the coexistence region of the species.

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