A dynamic model describing heterotrophic culture of chorella and its stability analysis
Chlorella is an important species of microorganism, whichincludes about 10 species. Chlorella USTB01 is a strain ofmicroalga which is isolated from Qinghe River in Beijing and hasstrong ability in the utilization of organic compounds and wasidentified as Chlorella sp. (H. Yan etal, Isolation andhete...
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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.2011.8.1117 |
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| author | Yan Zhang Wanbiao Ma Hai Yan Yasuhiro Takeuchi |
| author_facet | Yan Zhang Wanbiao Ma Hai Yan Yasuhiro Takeuchi |
| author_sort | Yan Zhang |
| collection | DOAJ |
| description | Chlorella is an important species of microorganism, whichincludes about 10 species. Chlorella USTB01 is a strain ofmicroalga which is isolated from Qinghe River in Beijing and hasstrong ability in the utilization of organic compounds and wasidentified as Chlorella sp. (H. Yan etal, Isolation andheterotrophic culture of Chlorella sp., J. Univ. Sci.Tech. Beijing, 2005, 27:408-412). In this paper, based on thestandard Chemostat models and the experimental data on theheterotrophic culture of Chlorella USTB01, a dynamic modelgoverned by differential equations with three variables (Chlorella, carbon source and nitrogen source) is proposed. For themodel, there always exists a boundary equilibrium, i.e.Chlorella-free equilibrium. Furthermore, underadditional conditions, the model also has the positive equilibria,i.e., the equilibira for which Chlorella, carbon source andnitrogen source are coexistent. Then, local and global asymptoticstability of the equilibria of the model have been discussed.Finally, the parameters in the model are determined according to theexperimental data, and numerical simulations are given. Thenumerical simulations show that the trajectories of the modelfit the trends of the experimental data well. |
| format | Article |
| id | doaj-art-347e6b4c292748e5a20d6c935129c8d0 |
| 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-347e6b4c292748e5a20d6c935129c8d02025-01-24T02:02:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-07-01841117113310.3934/mbe.2011.8.1117A dynamic model describing heterotrophic culture of chorella and its stability analysisYan Zhang0Wanbiao Ma1Hai Yan2Yasuhiro Takeuchi3Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083Chlorella is an important species of microorganism, whichincludes about 10 species. Chlorella USTB01 is a strain ofmicroalga which is isolated from Qinghe River in Beijing and hasstrong ability in the utilization of organic compounds and wasidentified as Chlorella sp. (H. Yan etal, Isolation andheterotrophic culture of Chlorella sp., J. Univ. Sci.Tech. Beijing, 2005, 27:408-412). In this paper, based on thestandard Chemostat models and the experimental data on theheterotrophic culture of Chlorella USTB01, a dynamic modelgoverned by differential equations with three variables (Chlorella, carbon source and nitrogen source) is proposed. For themodel, there always exists a boundary equilibrium, i.e.Chlorella-free equilibrium. Furthermore, underadditional conditions, the model also has the positive equilibria,i.e., the equilibira for which Chlorella, carbon source andnitrogen source are coexistent. Then, local and global asymptoticstability of the equilibria of the model have been discussed.Finally, the parameters in the model are determined according to theexperimental data, and numerical simulations are given. Thenumerical simulations show that the trajectories of the modelfit the trends of the experimental data well.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1117carbon sourcedifferential equationchlorellanitrogen sourcestability. |
| spellingShingle | Yan Zhang Wanbiao Ma Hai Yan Yasuhiro Takeuchi A dynamic model describing heterotrophic culture of chorella and its stability analysis Mathematical Biosciences and Engineering carbon source differential equation chlorella nitrogen source stability. |
| title | A dynamic model describing heterotrophic culture of chorella and its stability analysis |
| title_full | A dynamic model describing heterotrophic culture of chorella and its stability analysis |
| title_fullStr | A dynamic model describing heterotrophic culture of chorella and its stability analysis |
| title_full_unstemmed | A dynamic model describing heterotrophic culture of chorella and its stability analysis |
| title_short | A dynamic model describing heterotrophic culture of chorella and its stability analysis |
| title_sort | dynamic model describing heterotrophic culture of chorella and its stability analysis |
| topic | carbon source differential equation chlorella nitrogen source stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.1117 |
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