Center-manifold reduction for spiral waves

✍ Scribed by Björn Sandstede; Arnd Scheel; Claudia Wulff

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 503 KB
• Volume: 324
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)80335-8

✦ Synopsis

Spiral waves are rotating waves of reaction-diffusion equations on the plane. In this Note, a center-manifold reduction for the dynamics of spiral waves is presented. Bifurcations of rigidly-rotating spiral waves are then described by ordinary differential equations, which are equivarianr under the (special) Euclidean group SE(2). Several difficulties arise in this analysis because SE(2) IS not compact and does not induce a strongly continuous group action on the underlying function space, 0764.