Competition for a single resource and coexistence of several species in the chemostat
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 t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016012 |
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| author | Nahla Abdellatif Radhouane Fekih-Salem Tewfik Sari |
| author_facet | Nahla Abdellatif Radhouane Fekih-Salem Tewfik Sari |
| author_sort | Nahla Abdellatif |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7349a92760ef4e3ca7593af020900156 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7349a92760ef4e3ca7593af0209001562025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113463165210.3934/mbe.2016012Competition for a single resource and coexistence of several species in the chemostatNahla Abdellatif0Radhouane Fekih-Salem1Tewfik Sari2Université de Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 TunisUniversité de Tunis El Manar, ENIT, LAMSIN, BP 37, Le Belvédère, 1002 TunisIRSTEA, UMR Itap, 361 rue Jean-François Breton, 34196 Montpellier, France, and Université de Haute Alsace, LMIA, 4 rue des frères Lumière, 68093 MulhouseWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2016012coexistenceintra-specificcompetitionchemostatoperating diagram. |
| spellingShingle | Nahla Abdellatif Radhouane Fekih-Salem Tewfik Sari Competition for a single resource and coexistence of several species in the chemostat Mathematical Biosciences and Engineering coexistence intra-specific competition chemostat operating diagram. |
| title | Competition for a single resource and coexistence of several species in the chemostat |
| title_full | Competition for a single resource and coexistence of several species in the chemostat |
| title_fullStr | Competition for a single resource and coexistence of several species in the chemostat |
| title_full_unstemmed | Competition for a single resource and coexistence of several species in the chemostat |
| title_short | Competition for a single resource and coexistence of several species in the chemostat |
| title_sort | competition for a single resource and coexistence of several species in the chemostat |
| topic | coexistence intra-specific competition chemostat operating diagram. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016012 |
| work_keys_str_mv | AT nahlaabdellatif competitionforasingleresourceandcoexistenceofseveralspeciesinthechemostat AT radhouanefekihsalem competitionforasingleresourceandcoexistenceofseveralspeciesinthechemostat AT tewfiksari competitionforasingleresourceandcoexistenceofseveralspeciesinthechemostat |