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.

我们得到了具有非线性扩散的Lotka-Volterra系统定态解的全局分支结构的一些数学信息。首先，我们研究了Dirichlet边界条件下具有交叉扩散的Lotka-Volterra竞争系统，得到了当交叉扩散项趋于无穷大时极限系统平稳解的子集的全局分支。我们还研究了与Lotka-Volterra系统相关的反应-扩散-平流系统，得到了当扩散项和平流项趋于无穷大时极限系统定常解的整体分支结构。

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

Positive solutions for Lotka–Volterra competition systems with large cross-diffusion

• DOI: 10.1080/00036811003627534
• 发表时间: 2010-06
• 期刊: Applicable Analysis
• 影响因子: 1.1
• 作者: Kousuke Kuto;Yoshio Yamada