The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge
The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcat...
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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/10.1155/2013/168340 |
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| _version_ | 1832566128964009984 |
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| author | Shaoli Wang Zhihao Ge |
| author_facet | Shaoli Wang Zhihao Ge |
| author_sort | Shaoli Wang |
| collection | DOAJ |
| description | The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results. |
| format | Article |
| id | doaj-art-55246eeba77741e58ca07a3db28dea47 |
| 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-55246eeba77741e58ca07a3db28dea472025-02-03T01:04:58ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/168340168340The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey RefugeShaoli Wang0Zhihao Ge1School of Mathematics and Information Sciences, Henan University, Kaifeng 475001, ChinaSchool of Mathematics and Information Sciences, Henan University, Kaifeng 475001, ChinaThe Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.http://dx.doi.org/10.1155/2013/168340 |
| spellingShingle | Shaoli Wang Zhihao Ge The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge Abstract and Applied Analysis |
| title | The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge |
| title_full | The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge |
| title_fullStr | The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge |
| title_full_unstemmed | The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge |
| title_short | The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge |
| title_sort | hopf bifurcation for a predator prey system with logistic growth and prey refuge |
| url | http://dx.doi.org/10.1155/2013/168340 |
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