Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects
This paper is concerned with a delayed predator-prey diffusion model with Neumann boundary conditions. We study the asymptotic stability of the positive constant steady state and the conditions for the existence of Hopf bifurcation. In particular, we show that large diffusivity has no effect on the...
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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/10.1155/2012/856725 |
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| _version_ | 1832552087902224384 |
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| author | Jia-Fang Zhang |
| author_facet | Jia-Fang Zhang |
| author_sort | Jia-Fang Zhang |
| collection | DOAJ |
| description | This paper is concerned with a delayed predator-prey diffusion model with Neumann boundary conditions. We study the asymptotic stability of the positive constant steady state and the conditions for the existence of Hopf bifurcation. In particular, we show that large diffusivity has no effect on the Hopf bifurcation, while small diffusivity can lead to the fact that spatially nonhomogeneous periodic solutions bifurcate from the positive constant steady-state solution when the system parameters are all spatially homogeneous. Meanwhile, we study the properties of the spatially nonhomogeneous periodic solutions applying normal form theory of partial functional differential equations (PFDEs). |
| format | Article |
| id | doaj-art-839f09309de94d1daa133b16f138cc5a |
| 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-839f09309de94d1daa133b16f138cc5a2025-02-03T05:59:38ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/856725856725Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion EffectsJia-Fang Zhang0School of Mathematics and Information Sciences, Henan University, Henan, Kaifeng 475001, ChinaThis paper is concerned with a delayed predator-prey diffusion model with Neumann boundary conditions. We study the asymptotic stability of the positive constant steady state and the conditions for the existence of Hopf bifurcation. In particular, we show that large diffusivity has no effect on the Hopf bifurcation, while small diffusivity can lead to the fact that spatially nonhomogeneous periodic solutions bifurcate from the positive constant steady-state solution when the system parameters are all spatially homogeneous. Meanwhile, we study the properties of the spatially nonhomogeneous periodic solutions applying normal form theory of partial functional differential equations (PFDEs).http://dx.doi.org/10.1155/2012/856725 |
| spellingShingle | Jia-Fang Zhang Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects Abstract and Applied Analysis |
| title | Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects |
| title_full | Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects |
| title_fullStr | Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects |
| title_full_unstemmed | Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects |
| title_short | Spatially Nonhomogeneous Periodic Solutions in a Delayed Predator-Prey Model with Diffusion Effects |
| title_sort | spatially nonhomogeneous periodic solutions in a delayed predator prey model with diffusion effects |
| url | http://dx.doi.org/10.1155/2012/856725 |
| work_keys_str_mv | AT jiafangzhang spatiallynonhomogeneousperiodicsolutionsinadelayedpredatorpreymodelwithdiffusioneffects |