Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays
A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using...
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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/10.1155/2013/321930 |
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| _version_ | 1832563614834229248 |
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| author | Huitao Zhao Yiping Lin Yunxian Dai |
| author_facet | Huitao Zhao Yiping Lin Yunxian Dai |
| author_sort | Huitao Zhao |
| collection | DOAJ |
| description | A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included. |
| format | Article |
| id | doaj-art-0f70035d06704671a8a5dcf37f4676d1 |
| 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-0f70035d06704671a8a5dcf37f4676d12025-02-03T01:13:04ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/321930321930Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time DelaysHuitao Zhao0Yiping Lin1Yunxian Dai2Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaDepartment of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, ChinaA ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.http://dx.doi.org/10.1155/2013/321930 |
| spellingShingle | Huitao Zhao Yiping Lin Yunxian Dai Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays Abstract and Applied Analysis |
| title | Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays |
| title_full | Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays |
| title_fullStr | Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays |
| title_full_unstemmed | Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays |
| title_short | Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays |
| title_sort | stability and global hopf bifurcation analysis on a ratio dependent predator prey model with two time delays |
| url | http://dx.doi.org/10.1155/2013/321930 |
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