CROSS-DIFFUSION INDUCED INSTABILITY AND STABILITY IN REACTION-DIFFUSION SYSTEMS

被引：0

作者：

Shi, Junping ^{[1
,2
]}

Xie, Zhifu ^{[3
]}

Little, Kristina ^{[1
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

[2] Harbin Normal Univ, YY Tseng Funct Anal Res Ctr, Harbin 150025, Heilongjiang, Peoples R China

[3] Virginia State Univ, Dept Math & Comp Sci, Petersburg, VA 23806 USA

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2011年 / 1卷 / 01期

基金：

美国国家科学基金会;

关键词：

Reaction-diffusion systems; instability; cross-diffusion; pattern formation;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which is stable for the kinetic system but unstable for the self-diffusion reaction system. Application is given to predator-prey system with preytaxis and vegetation pattern formation in a water-limited ecosystem.

引用

页码：95 / 119

页数：25

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