Effects of spatial structure and diffusion on the performances of the chemostat
Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the i...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.953 |
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| _version_ | 1832590193923719168 |
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| author | Ihab Haidar Alain Rapaport Frédéric Gérard |
| author_facet | Ihab Haidar Alain Rapaport Frédéric Gérard |
| author_sort | Ihab Haidar |
| collection | DOAJ |
| description | Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models. |
| format | Article |
| id | doaj-art-7a58ed6f98bd430dae9d76316e6156af |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7a58ed6f98bd430dae9d76316e6156af2025-01-24T02:02:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-07-018495397110.3934/mbe.2011.8.953Effects of spatial structure and diffusion on the performances of the chemostatIhab Haidar0Alain Rapaport1Frédéric Gérard2UMR INRA/SupAgro 'MISTEA' and EPI INRA/INRIA 'MODEMIC', 2, pl. Viala 34060, MontpellierUMR INRA/SupAgro 'MISTEA' and EPI INRA/INRIA 'MODEMIC', 2, pl. Viala 34060, MontpellierUMR INRA/SupAgro 'MISTEA' and EPI INRA/INRIA 'MODEMIC', 2, pl. Viala 34060, MontpellierGiven hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.953global stability.chemostat modelinterconnectiondiffusion |
| spellingShingle | Ihab Haidar Alain Rapaport Frédéric Gérard Effects of spatial structure and diffusion on the performances of the chemostat Mathematical Biosciences and Engineering global stability. chemostat model interconnection diffusion |
| title | Effects of spatial structure and diffusion on the performances of the chemostat |
| title_full | Effects of spatial structure and diffusion on the performances of the chemostat |
| title_fullStr | Effects of spatial structure and diffusion on the performances of the chemostat |
| title_full_unstemmed | Effects of spatial structure and diffusion on the performances of the chemostat |
| title_short | Effects of spatial structure and diffusion on the performances of the chemostat |
| title_sort | effects of spatial structure and diffusion on the performances of the chemostat |
| topic | global stability. chemostat model interconnection diffusion |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.953 |
| work_keys_str_mv | AT ihabhaidar effectsofspatialstructureanddiffusionontheperformancesofthechemostat AT alainrapaport effectsofspatialstructureanddiffusionontheperformancesofthechemostat AT fredericgerard effectsofspatialstructureanddiffusionontheperformancesofthechemostat |