Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge
A diffusive predator-prey model with Holling type II functionalresponse and the no-flux boundary condition incorporating aconstant prey refuge is considered. Globally asymptoticallystability of the positive equilibrium is obtained. Regarding theconstant number of prey refuge $m$ as a bifurcation par...
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AIMS Press
2013-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.979 |
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| author | Xiaoyuan Chang Junjie Wei |
| author_facet | Xiaoyuan Chang Junjie Wei |
| author_sort | Xiaoyuan Chang |
| collection | DOAJ |
| description | A diffusive predator-prey model with Holling type II functionalresponse and the no-flux boundary condition incorporating aconstant prey refuge is considered. Globally asymptoticallystability of the positive equilibrium is obtained. Regarding theconstant number of prey refuge $m$ as a bifurcation parameter, byanalyzing the distribution of the eigenvalues, the existence ofHopf bifurcation is given. Employing the center manifold theoryand normal form method, an algorithm for determining theproperties of the Hopf bifurcation is derived. Some numericalsimulations for illustrating the analysis results are carried out. |
| format | Article |
| id | doaj-art-9cbd607f5900442fbce3ab3bce9c9e4b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9cbd607f5900442fbce3ab3bce9c9e4b2025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-0110497999610.3934/mbe.2013.10.979Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refugeXiaoyuan Chang0Junjie Wei1Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001A diffusive predator-prey model with Holling type II functionalresponse and the no-flux boundary condition incorporating aconstant prey refuge is considered. Globally asymptoticallystability of the positive equilibrium is obtained. Regarding theconstant number of prey refuge $m$ as a bifurcation parameter, byanalyzing the distribution of the eigenvalues, the existence ofHopf bifurcation is given. Employing the center manifold theoryand normal form method, an algorithm for determining theproperties of the Hopf bifurcation is derived. Some numericalsimulations for illustrating the analysis results are carried out.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.979hopf bifurcationprey refugeholling ii functional responsediffusion. |
| spellingShingle | Xiaoyuan Chang Junjie Wei Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge Mathematical Biosciences and Engineering hopf bifurcation prey refuge holling ii functional response diffusion. |
| title | Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge |
| title_full | Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge |
| title_fullStr | Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge |
| title_full_unstemmed | Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge |
| title_short | Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge |
| title_sort | stability and hopf bifurcation in a diffusivepredator prey system incorporating a prey refuge |
| topic | hopf bifurcation prey refuge holling ii functional response diffusion. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.979 |
| work_keys_str_mv | AT xiaoyuanchang stabilityandhopfbifurcationinadiffusivepredatorpreysystemincorporatingapreyrefuge AT junjiewei stabilityandhopfbifurcationinadiffusivepredatorpreysystemincorporatingapreyrefuge |