Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters
A class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the d...
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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/10.1155/2012/264870 |
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| _version_ | 1832558180116201472 |
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| author | Changjin Xu |
| author_facet | Changjin Xu |
| author_sort | Changjin Xu |
| collection | DOAJ |
| description | A class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. Finally, numerical simulations are performed to verify the analytical results. |
| format | Article |
| id | doaj-art-65217cf52a104006b6bcca38963003ba |
| 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-65217cf52a104006b6bcca38963003ba2025-02-03T01:32:58ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/264870264870Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent ParametersChangjin Xu0Guizhou Key Laboratory of Economics System Simulation, School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550004, ChinaA class of stage-structured predator-prey model with time delay and delay-dependent parameters is considered. Its linear stability is investigated and Hopf bifurcation is demonstrated. Using normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained. Finally, numerical simulations are performed to verify the analytical results.http://dx.doi.org/10.1155/2012/264870 |
| spellingShingle | Changjin Xu Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters Abstract and Applied Analysis |
| title | Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters |
| title_full | Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters |
| title_fullStr | Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters |
| title_full_unstemmed | Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters |
| title_short | Bifurcation Analysis for a Predator-Prey Model with Time Delay and Delay-Dependent Parameters |
| title_sort | bifurcation analysis for a predator prey model with time delay and delay dependent parameters |
| url | http://dx.doi.org/10.1155/2012/264870 |
| work_keys_str_mv | AT changjinxu bifurcationanalysisforapredatorpreymodelwithtimedelayanddelaydependentparameters |