Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System
A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction, the normal form theory, and the formulae deve...
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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/10.1155/2013/605471 |
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| _version_ | 1832552167798472704 |
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| author | Xia Liu Jinling Wang |
| author_facet | Xia Liu Jinling Wang |
| author_sort | Xia Liu |
| collection | DOAJ |
| description | A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction, the normal form theory, and the formulae developed by Xu and Huang, 2008 and Qiao et al., 2010, the normal forms and the versal unfoldings for this singularity are presented. The Hopf bifurcation of the system at another interior equilibrium is analyzed by taking delay (small or large) as bifurcation parameter. |
| format | Article |
| id | doaj-art-8627b0e1463d4015a87c83b6f350298a |
| 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-8627b0e1463d4015a87c83b6f350298a2025-02-03T05:59:26ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/605471605471Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey SystemXia Liu0Jinling Wang1College of Mathematics and Information Science, Henan Normal University, 453007, ChinaCollege of Mathematics and Information Science, Henan Normal University, 453007, ChinaA delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction, the normal form theory, and the formulae developed by Xu and Huang, 2008 and Qiao et al., 2010, the normal forms and the versal unfoldings for this singularity are presented. The Hopf bifurcation of the system at another interior equilibrium is analyzed by taking delay (small or large) as bifurcation parameter.http://dx.doi.org/10.1155/2013/605471 |
| spellingShingle | Xia Liu Jinling Wang Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System Abstract and Applied Analysis |
| title | Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System |
| title_full | Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System |
| title_fullStr | Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System |
| title_full_unstemmed | Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System |
| title_short | Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System |
| title_sort | bogdanov takens and triple zero bifurcations of a delayed modified leslie gower predator prey system |
| url | http://dx.doi.org/10.1155/2013/605471 |
| work_keys_str_mv | AT xialiu bogdanovtakensandtriplezerobifurcationsofadelayedmodifiedlesliegowerpredatorpreysystem AT jinlingwang bogdanovtakensandtriplezerobifurcationsofadelayedmodifiedlesliegowerpredatorpreysystem |