Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System
The dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey system subject to Neumann boundary conditions are considered. By choosing the ratio of intrinsic growth rates of predators to preys as a bifurcation parameter, the existence and stability of spatially homogeneous and nonhomogen...
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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/10.1155/2013/592547 |
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| _version_ | 1849413193651191808 |
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| author | Wenjie Zuo |
| author_facet | Wenjie Zuo |
| author_sort | Wenjie Zuo |
| collection | DOAJ |
| description | The dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey system subject to Neumann boundary conditions are considered. By choosing the ratio of intrinsic growth rates of predators to preys as a bifurcation parameter, the existence and stability of spatially homogeneous and nonhomogeneous Hopf bifurcations and steady state bifurcation are investigated in detail. Meanwhile, we show that Turing instability takes place at a certain critical value; that is, the stationary solution becomes unstable induced by diffusion. Particularly, the sufficient conditions of the global stability of the positive constant coexistence are given by the upper-lower solutions method. |
| format | Article |
| id | doaj-art-74e0635b683b43e0b1e72d0ed5ea3b44 |
| 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-74e0635b683b43e0b1e72d0ed5ea3b442025-08-20T03:34:12ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/592547592547Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner SystemWenjie Zuo0College of Science, China University of Petroleum (East China), Qingdao, Shandong 266580, ChinaThe dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey system subject to Neumann boundary conditions are considered. By choosing the ratio of intrinsic growth rates of predators to preys as a bifurcation parameter, the existence and stability of spatially homogeneous and nonhomogeneous Hopf bifurcations and steady state bifurcation are investigated in detail. Meanwhile, we show that Turing instability takes place at a certain critical value; that is, the stationary solution becomes unstable induced by diffusion. Particularly, the sufficient conditions of the global stability of the positive constant coexistence are given by the upper-lower solutions method.http://dx.doi.org/10.1155/2013/592547 |
| spellingShingle | Wenjie Zuo Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System Abstract and Applied Analysis |
| title | Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System |
| title_full | Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System |
| title_fullStr | Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System |
| title_full_unstemmed | Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System |
| title_short | Global Stability and Bifurcations of a Diffusive Ratio-Dependent Holling-Tanner System |
| title_sort | global stability and bifurcations of a diffusive ratio dependent holling tanner system |
| url | http://dx.doi.org/10.1155/2013/592547 |
| work_keys_str_mv | AT wenjiezuo globalstabilityandbifurcationsofadiffusiveratiodependenthollingtannersystem |