Qualitative Analysis on a Reaction-Diffusion Prey-Predator Model and the Corresponding Steady-States
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-sta...
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| Published in | Chinese annals of mathematics. Serie B Vol. 30; no. 2; pp. 207 - 220 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer-Verlag
01.03.2009
Department of Mathematics,College of Science,China Three Gorges University,Yichang 443002,Hubei,China |
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| Abstract | The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for nonexistence of positive non-constant steady-states are derived. |
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| AbstractList | The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for nonexistence of positive non-constant steady-states are derived. O1; The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived. The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non-existence of positive non-constant steady-states are derived. |
| Author | Qunyi BIE Rui PENG |
| AuthorAffiliation | Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, Hubei, China |
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| Cites_doi | 10.1016/j.aml.2006.08.020 10.1016/S0022-0396(02)00100-6 10.1006/jdeq.1996.0157 10.1016/j.jde.2004.05.010 10.1126/science.171.3969.385 10.1017/S0308210500004704 10.1016/0022-0396(88)90147-7 10.1137/S0036139901393494 10.2307/1936296 10.1017/S0308210500002742 10.1016/j.jde.2004.01.004 10.1017/S0308210500003814 10.1137/S0036139993253201 10.1137/S0036139997318457 10.1007/BF02459707 10.1007/BFb0089647 |
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| Keywords | 92D25 Global stability Non-existence 37B25 Steady-state Prey-predator model 35J55 |
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| Notes | Q141 31-1329/O1 Prey-predator model, Steady-state, Global stability, Non-existence O175.2 |
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| Title | Qualitative Analysis on a Reaction-Diffusion Prey-Predator Model and the Corresponding Steady-States |
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