Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator
A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an itera...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/285934 |
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| _version_ | 1832565362482216960 |
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| author | Xiao Zhang Rui Xu Qintao Gan |
| author_facet | Xiao Zhang Rui Xu Qintao Gan |
| author_sort | Xiao Zhang |
| collection | DOAJ |
| description | A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-28daf36664f34441856d1d8a71b75fc6 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-28daf36664f34441856d1d8a71b75fc62025-02-03T01:07:50ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/285934285934Global Stability for a Delayed Predator-Prey System with Stage Structure for the PredatorXiao Zhang0Rui Xu1Qintao Gan2Institute of Applied Mathematics, Shijiazhaung Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhaung Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhaung Mechanical Engineering College, Shijiazhuang 050003, ChinaA delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.http://dx.doi.org/10.1155/2009/285934 |
| spellingShingle | Xiao Zhang Rui Xu Qintao Gan Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator Discrete Dynamics in Nature and Society |
| title | Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator |
| title_full | Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator |
| title_fullStr | Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator |
| title_full_unstemmed | Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator |
| title_short | Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator |
| title_sort | global stability for a delayed predator prey system with stage structure for the predator |
| url | http://dx.doi.org/10.1155/2009/285934 |
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