The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat
A mathematical model involving a syntrophic relationship between two populationsof bacteria in a continuous culture is proposed. A detailed qualitative analysis iscarried out as well as the analysis of the local and global stability of the equilibria.We demonstrate, under general assumptions of mono...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.627 |
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| author | Tewfik Sari Miled El Hajji Jérôme Harmand |
| author_facet | Tewfik Sari Miled El Hajji Jérôme Harmand |
| author_sort | Tewfik Sari |
| collection | DOAJ |
| description | A mathematical model involving a syntrophic relationship between two populationsof bacteria in a continuous culture is proposed. A detailed qualitative analysis iscarried out as well as the analysis of the local and global stability of the equilibria.We demonstrate, under general assumptions of monotonicity which are relevant froman applied point of view, the asymptotic stability of the positiveequilibrium point which corresponds to the coexistence of the two bacteria.A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model. |
| format | Article |
| id | doaj-art-f50a3f2e48dc43a0b149c2ed3e4403db |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f50a3f2e48dc43a0b149c2ed3e4403db2025-01-24T02:07:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-06-019362764510.3934/mbe.2012.9.627The mathematical analysis of a syntrophic relationship between two microbial species in a chemostatTewfik Sari0Miled El Hajji1Jérôme Harmand2Irstea, UMR ITAP, 361 rue Jean-François Breton 34196 Montpellier, & Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 MontpellierIrstea, UMR ITAP, 361 rue Jean-François Breton 34196 Montpellier, & Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 MontpellierIrstea, UMR ITAP, 361 rue Jean-François Breton 34196 Montpellier, & Modemic (Inra/Inria), UMR Mistea, 2 place Viala, 34060 MontpellierA mathematical model involving a syntrophic relationship between two populationsof bacteria in a continuous culture is proposed. A detailed qualitative analysis iscarried out as well as the analysis of the local and global stability of the equilibria.We demonstrate, under general assumptions of monotonicity which are relevant froman applied point of view, the asymptotic stability of the positiveequilibrium point which corresponds to the coexistence of the two bacteria.A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.627global asymptotic stabilitysyntrophic relationshipcoexistencechemostatanaerobic digestion. |
| spellingShingle | Tewfik Sari Miled El Hajji Jérôme Harmand The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat Mathematical Biosciences and Engineering global asymptotic stability syntrophic relationship coexistence chemostat anaerobic digestion. |
| title | The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat |
| title_full | The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat |
| title_fullStr | The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat |
| title_full_unstemmed | The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat |
| title_short | The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat |
| title_sort | mathematical analysis of a syntrophic relationship between two microbial species in a chemostat |
| topic | global asymptotic stability syntrophic relationship coexistence chemostat anaerobic digestion. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.627 |
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