Study on spatial pattern solutions for the Lotka-Volterra system with advection

Lotka-Volterra系统平流空间格局解研究

• 批准号: 21740129
• 负责人: KUTO Kousuke
• 金额: $ 2.75万
• 依托单位: The University of Electro-Communications (2010-2011)Fukuoka Institute of Technology (2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740129/
• 关键词: 非線形数理; 反応拡散移流系; 定常解; 分岐; 数理生物モデル; 極限系; 移流; 反応拡散; 楕円型偏微分方程式; 境界条件; 現象の数理; ロトカ・ボルテラ系; 反応拡散系; 定常パターン; 数理モデル; 相互拡散; アプリオリ評価; 漸近解析; 写像度

We derive some mathematical information on the global bifurcation structure of stationary solutions to the Lotka-Volterra system with nonlinear diffusion. First we study the Lotka-Volterra competition system with cross-diffusion under the Dirichlet boundary conditions to obtain the global bifurcation branch of a subset of stationary solutions to the limiting system as a cross-diffusion term tends to infinity. We also study a reaction-diffusion-advection system related to the Lotka-Volterra system and obtain the global bifurcation structure of stationary solutions to the limiting system as the diffusion and advection terms tend to infinity.

我们得出了一些数学信息，这些信息与非线性扩散的Lotka-Volterra系统的固定解的全局分叉结构。首先，我们研究了在Dirichlet边界条件下具有交叉扩散的Lotka-Volterra竞争系统，以获取固定溶液子集的全球分叉分支到限制系统的一部分，作为交叉扩散项倾向于无限。我们还研究了与Lotka-Volterra系统相关的反应扩散 - 介导系统，并获得限制系统固定溶液的全球分叉结构，因为扩散和对流术语往往是无限的。

项目成果

Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type

• DOI: 10.57262/die/1356019545
• 发表时间: 2009-07
• 期刊: Differential and Integral Equations
• 影响因子: 1.4
• 作者: Kousuke Kuto;Yoshio Yamada