On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays
A ratio-dependent predator-prey model with two delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are obtained. It shows that the two different time delays have different effects on the dynamical beh...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/679602 |
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| _version_ | 1832565751171514368 |
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| author | Changjin Xu Yusen Wu |
| author_facet | Changjin Xu Yusen Wu |
| author_sort | Changjin Xu |
| collection | DOAJ |
| description | A ratio-dependent predator-prey model with two delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are obtained. It shows that the two different time delays have different effects on the dynamical behavior of the system. An example together with its numerical simulations shows the feasibility of the main results. Finally, main conclusions are included. |
| format | Article |
| id | doaj-art-e6c0f223b1ce4a359f2b2df0665ab11f |
| 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-e6c0f223b1ce4a359f2b2df0665ab11f2025-02-03T01:06:54ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/679602679602On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with DelaysChangjin Xu0Yusen Wu1Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, ChinaDepartment of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, ChinaA ratio-dependent predator-prey model with two delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are obtained. It shows that the two different time delays have different effects on the dynamical behavior of the system. An example together with its numerical simulations shows the feasibility of the main results. Finally, main conclusions are included.http://dx.doi.org/10.1155/2013/679602 |
| spellingShingle | Changjin Xu Yusen Wu On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays Journal of Applied Mathematics |
| title | On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays |
| title_full | On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays |
| title_fullStr | On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays |
| title_full_unstemmed | On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays |
| title_short | On the Nature of Bifurcation in a Ratio-Dependent Predator-Prey Model with Delays |
| title_sort | on the nature of bifurcation in a ratio dependent predator prey model with delays |
| url | http://dx.doi.org/10.1155/2013/679602 |
| work_keys_str_mv | AT changjinxu onthenatureofbifurcationinaratiodependentpredatorpreymodelwithdelays AT yusenwu onthenatureofbifurcationinaratiodependentpredatorpreymodelwithdelays |