Global dynamics of the chemostat with different removal rates and variable yields
In this paper, we consider a competition model between $n$ species in a chemostat includingboth monotone and non-monotone growth functions, distinct removal rates and variable yields.We show that only the species with the lowest break-even concentration survives, provided that additional technicalco...
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AIMS Press
2011-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.827 |
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| author | Tewfik Sari Frederic Mazenc |
| author_facet | Tewfik Sari Frederic Mazenc |
| author_sort | Tewfik Sari |
| collection | DOAJ |
| description | In this paper, we consider a competition model between $n$ species in a chemostat includingboth monotone and non-monotone growth functions, distinct removal rates and variable yields.We show that only the species with the lowest break-even concentration survives, provided that additional technicalconditions on the growth functions and yields are satisfied.We construct a Lyapunov function which reduces to the Lyapunov function used byS. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growthfunctions are of Michaelis-Menten type and the yields are constant.Various applications are given including linear, quadratic and cubic yields. |
| format | Article |
| id | doaj-art-bd471306d6f44c559c0c40add35d9f00 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-bd471306d6f44c559c0c40add35d9f002025-01-24T02:01:59ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-05-018382784010.3934/mbe.2011.8.827Global dynamics of the chemostat with different removal rates and variable yieldsTewfik Sari0Frederic Mazenc1Université de Haute Alsace, MulhouseUniversité de Haute Alsace, MulhouseIn this paper, we consider a competition model between $n$ species in a chemostat includingboth monotone and non-monotone growth functions, distinct removal rates and variable yields.We show that only the species with the lowest break-even concentration survives, provided that additional technicalconditions on the growth functions and yields are satisfied.We construct a Lyapunov function which reduces to the Lyapunov function used byS. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growthfunctions are of Michaelis-Menten type and the yields are constant.Various applications are given including linear, quadratic and cubic yields.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.827lyapunov functioncompetitive exclusion principlechemostatglobal asymptotic stabilityvariable yield model. |
| spellingShingle | Tewfik Sari Frederic Mazenc Global dynamics of the chemostat with different removal rates and variable yields Mathematical Biosciences and Engineering lyapunov function competitive exclusion principle chemostat global asymptotic stability variable yield model. |
| title | Global dynamics of the chemostat with different removal rates and variable yields |
| title_full | Global dynamics of the chemostat with different removal rates and variable yields |
| title_fullStr | Global dynamics of the chemostat with different removal rates and variable yields |
| title_full_unstemmed | Global dynamics of the chemostat with different removal rates and variable yields |
| title_short | Global dynamics of the chemostat with different removal rates and variable yields |
| title_sort | global dynamics of the chemostat with different removal rates and variable yields |
| topic | lyapunov function competitive exclusion principle chemostat global asymptotic stability variable yield model. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.827 |
| work_keys_str_mv | AT tewfiksari globaldynamicsofthechemostatwithdifferentremovalratesandvariableyields AT fredericmazenc globaldynamicsofthechemostatwithdifferentremovalratesandvariableyields |