Document Type

Article

Publication Date

2-1-1992

Publication Title

SIAM Journal on Applied Mathematics

Abstract

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.

Volume

52

Issue

1

First Page Number

181

Last Page Number

221

DOI

10.1137/0152011

Publisher Statement

© 1992, SIAM Publications.

Included in

Mathematics Commons

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