ROTATING CHEMICAL WAVES IN THE GRAY-SCOTT MODEL

被引：9

作者：

FARR, WW ^{[1
]}

GOLUBITSKY, M ^{[1
]}

机构：

[1] UNIV HOUSTON,DEPT MATH,HOUSTON,TX 77204

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1992年 / 52卷 / 01期

关键词：

HOPF BIFURCATION; O(2) SYMMETRY; REACTION-DIFFUSION EQUATIONS; NORMAL FORM REDUCTION; ROTATING (TRAVELING) WAVES; MODE INTERACTIONS; GRAY-SCOTT MODEL;

D O I：

10.1137/0152011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A set of reaction-diffusion equations is considered, known as the Gray-Scott model, defined on a circle, and the stability of rotating wave solutions formed via Hopf bifurcations that break the circular O(2) symmetry is investigated. Using a hybrid numerical/analytical technique, center manifold/normal form reductions are performed to analyze symmetry-breaking Hopf bifurcations, degenerate Hopf bifurcations, and Hopf-Hopf mode interactions. It is found that stable rotating waves exist over broad ranges of parameter values and that the bifurcation behavior of this relatively simple model can be quite complex, e.g., two- and three-frequency motions exist.

引用

页码：181 / 221

页数：41