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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Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 30; no. 2; pp. 207 - 220
Main Authors Bie, Qunyi, Peng, Rui
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.03.2009
Department of Mathematics,College of Science,China Three Gorges University,Yichang 443002,Hubei,China
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Neumann边界条件
反应扩散系统
定性描述
捕食模型
稳定状态
非恒定
92D25
Global stability
Non-existence
37B25
Steady-state
Prey-predator model
35J55
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Summary: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.
Bibliography:Q141
31-1329/O1
Prey-predator model, Steady-state, Global stability, Non-existence
O175.2
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-007-0027-0