Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the sa...
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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/10.1155/2013/478315 |
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| _version_ | 1832545602889580544 |
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| author | Xia Liu Yepeng Xing |
| author_facet | Xia Liu Yepeng Xing |
| author_sort | Xia Liu |
| collection | DOAJ |
| description | The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting. |
| format | Article |
| id | doaj-art-c32e8cd27ee4419ba41b0244ce8576b0 |
| 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-c32e8cd27ee4419ba41b0244ce8576b02025-02-03T07:25:21ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/478315478315Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant HarvestingXia Liu0Yepeng Xing1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaCollege of Mathematics and Science, Shanghai Normal University, Shanghai 200234, ChinaThe bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting.http://dx.doi.org/10.1155/2013/478315 |
| spellingShingle | Xia Liu Yepeng Xing Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting Abstract and Applied Analysis |
| title | Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting |
| title_full | Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting |
| title_fullStr | Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting |
| title_full_unstemmed | Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting |
| title_short | Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting |
| title_sort | bifurcations of a ratio dependent holling tanner system with refuge and constant harvesting |
| url | http://dx.doi.org/10.1155/2013/478315 |
| work_keys_str_mv | AT xialiu bifurcationsofaratiodependenthollingtannersystemwithrefugeandconstantharvesting AT yepengxing bifurcationsofaratiodependenthollingtannersystemwithrefugeandconstantharvesting |