Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production
The work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the s...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/354095 |
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| _version_ | 1832565100397985792 |
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| author | Chunjin Wei Shuwen Zhang Lansun Chen |
| author_facet | Chunjin Wei Shuwen Zhang Lansun Chen |
| author_sort | Chunjin Wei |
| collection | DOAJ |
| description | The work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate, and the initial concentrate of microorganism and substrate. For some special cases, it is also shown that the system may exist in order-2 periodic solution. Furthermore, our findings are confirmed by means of numerical simulations. |
| format | Article |
| id | doaj-art-56017977c07a4f329a9e997aa8767df3 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-56017977c07a4f329a9e997aa8767df32025-02-03T01:09:25ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/354095354095Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein ProductionChunjin Wei0Shuwen Zhang1Lansun Chen2Science College, Jimei University, Xiamen, Fujian 361021, ChinaScience College, Jimei University, Xiamen, Fujian 361021, ChinaAcademy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, ChinaThe work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate, and the initial concentrate of microorganism and substrate. For some special cases, it is also shown that the system may exist in order-2 periodic solution. Furthermore, our findings are confirmed by means of numerical simulations.http://dx.doi.org/10.1155/2013/354095 |
| spellingShingle | Chunjin Wei Shuwen Zhang Lansun Chen Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production Journal of Applied Mathematics |
| title | Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production |
| title_full | Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production |
| title_fullStr | Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production |
| title_full_unstemmed | Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production |
| title_short | Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production |
| title_sort | impulsive state feedback control of cheese whey fermentation for single cell protein production |
| url | http://dx.doi.org/10.1155/2013/354095 |
| work_keys_str_mv | AT chunjinwei impulsivestatefeedbackcontrolofcheesewheyfermentationforsinglecellproteinproduction AT shuwenzhang impulsivestatefeedbackcontrolofcheesewheyfermentationforsinglecellproteinproduction AT lansunchen impulsivestatefeedbackcontrolofcheesewheyfermentationforsinglecellproteinproduction |