Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay
A predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/252437 |
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| _version_ | 1832547496711159808 |
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| author | Yakui Xue Xiaoqing Wang |
| author_facet | Yakui Xue Xiaoqing Wang |
| author_sort | Yakui Xue |
| collection | DOAJ |
| description | A predator-prey system with disease in the predator is investigated, where the
discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local
analysis and Hopf bifurcation analysis. By analyzing the associated characteristic
equation, it is found that Hopf bifurcation occurs when τ crosses some critical values.
Using the normal form theory and center manifold argument, the explicit formulae
which determine the stability, direction, and other properties of bifurcating periodic
solutions are derived. |
| format | Article |
| id | doaj-art-3893885410414a848efa131426c6d083 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3893885410414a848efa131426c6d0832025-02-03T06:44:37ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/252437252437Stability and Local Hopf Bifurcation for a Predator-Prey Model with DelayYakui Xue0Xiaoqing Wang1Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, North University of China, Taiyuan, Shanxi 030051, ChinaA predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when τ crosses some critical values. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.http://dx.doi.org/10.1155/2012/252437 |
| spellingShingle | Yakui Xue Xiaoqing Wang Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay Discrete Dynamics in Nature and Society |
| title | Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay |
| title_full | Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay |
| title_fullStr | Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay |
| title_full_unstemmed | Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay |
| title_short | Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay |
| title_sort | stability and local hopf bifurcation for a predator prey model with delay |
| url | http://dx.doi.org/10.1155/2012/252437 |
| work_keys_str_mv | AT yakuixue stabilityandlocalhopfbifurcationforapredatorpreymodelwithdelay AT xiaoqingwang stabilityandlocalhopfbifurcationforapredatorpreymodelwithdelay |