Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism
We research the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stabil...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/829045 |
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| _version_ | 1832558506659545088 |
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| author | Haiyun Bai Yanhui Zhai |
| author_facet | Haiyun Bai Yanhui Zhai |
| author_sort | Haiyun Bai |
| collection | DOAJ |
| description | We research the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. Finally, some numerical simulations are given to illustrate the effectiveness of our results. |
| format | Article |
| id | doaj-art-2697c5bdaf3946af9dca00b40f0847a5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2697c5bdaf3946af9dca00b40f0847a52025-02-03T01:32:13ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/829045829045Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of OrganismHaiyun Bai0Yanhui Zhai1School of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaWe research the dynamics of the chemostat model with time delay. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. Finally, some numerical simulations are given to illustrate the effectiveness of our results.http://dx.doi.org/10.1155/2013/829045 |
| spellingShingle | Haiyun Bai Yanhui Zhai Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism Abstract and Applied Analysis |
| title | Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism |
| title_full | Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism |
| title_fullStr | Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism |
| title_full_unstemmed | Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism |
| title_short | Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism |
| title_sort | hopf bifurcation analysis for the model of the chemostat with one species of organism |
| url | http://dx.doi.org/10.1155/2013/829045 |
| work_keys_str_mv | AT haiyunbai hopfbifurcationanalysisforthemodelofthechemostatwithonespeciesoforganism AT yanhuizhai hopfbifurcationanalysisforthemodelofthechemostatwithonespeciesoforganism |