Stability and instability in the Gray-Scott model: The case of equal diffusivities

被引：36

作者：

Hale, JK ^{[1
]}

Peletier, LA

Troy, WC

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Leiden Univ, Inst Math, NL-2300 RA Leiden, Netherlands

[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

APPLIED MATHEMATICS LETTERS | 1999年 / 12卷 / 04期

关键词：

homoclinic orbits; heteroclinic orbits; stability; reaction-diffusion equations; Gray-Scott model;

D O I：

10.1016/S0893-9659(99)00035-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a family of explicit stationary homoclinic orbits of the Gray-Scott system of cubic autocatalysis is unstable, and that an explicit heteroclinic orbit of this system is asymptotically, and exponentially stable. (C) 1999 Elsevier Science Ltd. All rights reserved.

引用

页码：59 / 65

页数：7

共 19 条

[1]

DOCKERY JA, 1998, NUMERICAL EVIDENCE S

[2] Pattern formation in the one-dimensional Gray-Scott model [J].