Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays
A mathematical model for growth of tumors with two discrete delays is studied. The delays, respectively, represent the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis and kill of cells by the inhibitor. We show the influence of...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/980686 |
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| _version_ | 1832564520033189888 |
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| author | Bao Shi Fangwei Zhang Shihe Xu |
| author_facet | Bao Shi Fangwei Zhang Shihe Xu |
| author_sort | Bao Shi |
| collection | DOAJ |
| description | A mathematical model for growth of tumors with two discrete delays is studied. The delays,
respectively, represent the time taken for cells to undergo mitosis and the time taken for the cell to
modify the rate of cell loss due to apoptosis and kill of cells by the inhibitor. We show the influence
of time delays on the Hopf bifurcation when one of delays is used as a bifurcation parameter. |
| format | Article |
| id | doaj-art-121d70a44b3c485d9385a657745d8837 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-121d70a44b3c485d9385a657745d88372025-02-03T01:10:46ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/980686980686Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time DelaysBao Shi0Fangwei Zhang1Shihe Xu2Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong 264001, ChinaInstitute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong 264001, ChinaDepartment of Mathematics, Zhaoqing University, Zhaoqing, Guangdong 526061, ChinaA mathematical model for growth of tumors with two discrete delays is studied. The delays, respectively, represent the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis and kill of cells by the inhibitor. We show the influence of time delays on the Hopf bifurcation when one of delays is used as a bifurcation parameter.http://dx.doi.org/10.1155/2011/980686 |
| spellingShingle | Bao Shi Fangwei Zhang Shihe Xu Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays Abstract and Applied Analysis |
| title | Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays |
| title_full | Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays |
| title_fullStr | Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays |
| title_full_unstemmed | Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays |
| title_short | Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays |
| title_sort | hopf bifurcation of a mathematical model for growth of tumors with an action of inhibitor and two time delays |
| url | http://dx.doi.org/10.1155/2011/980686 |
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