Mathematical Analysis for competition between species in heterogeneous environment

异质环境中物种间竞争的数学分析

• 批准号: 20540109
• 负责人: NAKAMURA Ken-ichi
• 金额: $ 2.83万
• 依托单位: Kanazawa University (2011)The University of Electro-Communications (2008-2010)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540109/
• 关键词: 反応拡散系; 進行波解; 均質化極限; 界面方程式; 数理生態学; 進行波; 2種競争系

In this research project, for the mathematical study of competition between biological species in heterogeneous environment, we investigated the effect of spatial inhomogeneity on the propagating speed of traveling waves of 2-species Lotka-Volterra competition-diffusion systems and their singular limit equations. Among other things, we obtained sharp estimates of the average propagation speed of traveling waves in spatially periodic environment, showed the existence and the asymptotic stability of recurrent traveling waves and established conditions for the well-definedness of the average speed of the recurrent traveling wave. We also considered the homogenization problem and determined the homogenization limit of the average speed and the limit profile of the traveling waves

在本研究项目中，针对异质环境中生物种群间竞争的数学研究，我们研究了空间不均匀性对两种群Lotka-Volterra竞争扩散系统及其奇异极限方程行波传播速度的影响.其中，我们得到了空间周期环境中行波的平均传播速度的精确估计，证明了递归行波的存在性和渐近稳定性，并建立了递归行波的平均速度的良好定义的条件。我们还考虑了均匀化问题，确定了平均速度的均匀化极限和行波的极限轮廓

项目成果

Front propagation for Lotka-Volterra competitiondiffusion systems in a cylinder with spatially undulating boundary

具有空间起伏边界的圆柱体中 Lotka-Volterra 竞争扩散系统的前向传播

• 发表时间: 2008
• 作者: Y.Mochimaru;M-W.Bae;Ken-Ichi Nakamura;Yoshihiro Mochimaru;Y. Mochimaru & M-w. Bae;原田昌晃;Ken-Ichi Nakamura;Ken-Ichi Nakamura;Yoshihiro Mochimaru;小松彦三郎;Ken-Ichi Nakamura;Yoshihiro Mochimaru;Hikosaburo Komatsu;Ken-Ichi Nakamura;Hikosaburo Komatsu;Ken-Ichi Nakamura;Hikosaburo Komatsu;小松彦三郎;中村健一;小松彦三郎,田中由真著;中村健一;小松彦三郎;中 村 健 一;小松彦三郎;Ken-Ichi Nakamura
• 通讯作者: Ken-Ichi Nakamura

Asymptotic stability of traveling waves in heterogeneous media

异质介质中行波的渐近稳定性

• 发表时间: 2008
• 作者: Y.Mochimaru;M-W.Bae;Ken-Ichi Nakamura;Yoshihiro Mochimaru;Y. Mochimaru & M-w. Bae;原田昌晃;Ken-Ichi Nakamura;Ken-Ichi Nakamura;Yoshihiro Mochimaru;小松彦三郎;Ken-Ichi Nakamura;Yoshihiro Mochimaru;Hikosaburo Komatsu;Ken-Ichi Nakamura;Hikosaburo Komatsu;Ken-Ichi Nakamura
• 通讯作者: Ken-Ichi Nakamura

Existence of recurrent traveling waves in a two-dimensional cylinder with undulating boundary-the virtual pinning case

边界起伏的二维圆柱体中循环行波的存在性——虚拟钉扎情况

• 发表时间: 2011
• 作者: Y.Mochimaru;M-W.Bae;Ken-Ichi Nakamura
• 通讯作者: Ken-Ichi Nakamura

Homogenization limit of recurrent traveling waves in a two-dimensional cylinder with undulating boundary

边界起伏的二维圆柱体中循环行波的均匀化极限

• 发表时间: 2010
• 作者: Y.Mochimaru;M-W.Bae;Ken-Ichi Nakamura;Yoshihiro Mochimaru;Y. Mochimaru & M-w. Bae;原田昌晃;Ken-Ichi Nakamura;Ken-Ichi Nakamura
• 通讯作者: Ken-Ichi Nakamura

非一様な場を伝播する進行波の速度

行波在非均匀场中传播的速度

• 发表时间: 2008
• 作者: Masahiro HACHIMORI;Hiroshi KURATA;Tadashi SAKUMA;中村健一
• 通讯作者: 中村健一