Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System
A delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhães. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity....
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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/10.1155/2013/898015 |
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| _version_ | 1849414621034708992 |
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| author | Xia Liu Yanwei Liu Jinling Wang |
| author_facet | Xia Liu Yanwei Liu Jinling Wang |
| author_sort | Xia Liu |
| collection | DOAJ |
| description | A delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhães. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity. A versal unfolding of the system at this singularity is obtained. Our main results illustrate that the delay has an important effect on the dynamical behaviors of the system. |
| format | Article |
| id | doaj-art-6ba10842eeff4ef3a702d98e6d42b8e5 |
| 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-6ba10842eeff4ef3a702d98e6d42b8e52025-08-20T03:33:46ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/898015898015Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey SystemXia Liu0Yanwei Liu1Jinling Wang2College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaInstitute of Systems Biology, Shanghai University, Shanghai 200444, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaA delayed predator prey system with refuge and constant rate harvesting is discussed by applying the normal form theory of retarded functional differential equations introduced by Faria and Magalhães. The analysis results show that under some conditions the system has a Bogdanov-Takens singularity. A versal unfolding of the system at this singularity is obtained. Our main results illustrate that the delay has an important effect on the dynamical behaviors of the system.http://dx.doi.org/10.1155/2013/898015 |
| spellingShingle | Xia Liu Yanwei Liu Jinling Wang Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System Abstract and Applied Analysis |
| title | Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System |
| title_full | Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System |
| title_fullStr | Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System |
| title_full_unstemmed | Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System |
| title_short | Bogdanov-Takens Bifurcation of a Delayed Ratio-Dependent Holling-Tanner Predator Prey System |
| title_sort | bogdanov takens bifurcation of a delayed ratio dependent holling tanner predator prey system |
| url | http://dx.doi.org/10.1155/2013/898015 |
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