Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay
A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation....
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/363051 |
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| _version_ | 1849467784214347776 |
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| author | Shuang Guo Weihua Jiang |
| author_facet | Shuang Guo Weihua Jiang |
| author_sort | Shuang Guo |
| collection | DOAJ |
| description | A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results. |
| format | Article |
| id | doaj-art-e651b255dd5341c6bd55e2ae4704ed52 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e651b255dd5341c6bd55e2ae4704ed522025-08-20T03:26:04ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/363051363051Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with DelayShuang Guo0Weihua Jiang1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaA class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.http://dx.doi.org/10.1155/2012/363051 |
| spellingShingle | Shuang Guo Weihua Jiang Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay Abstract and Applied Analysis |
| title | Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay |
| title_full | Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay |
| title_fullStr | Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay |
| title_full_unstemmed | Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay |
| title_short | Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay |
| title_sort | hopf bifurcation analysis on general gause type predator prey models with delay |
| url | http://dx.doi.org/10.1155/2012/363051 |
| work_keys_str_mv | AT shuangguo hopfbifurcationanalysisongeneralgausetypepredatorpreymodelswithdelay AT weihuajiang hopfbifurcationanalysisongeneralgausetypepredatorpreymodelswithdelay |