Dynamics of spiral waves on unbounded domains using center-manifold reductions

Björn Sandstede, Arnd Scheel, Claudia Wulff

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67 Scopus citations

Abstract

An equivariant center-manifold reduction near relative equilibria of G-equivariant semiflows on Banach spaces is presented. In contrast to previous results, the Lie group G is possibly non-compact. Moreover, it is not required that G induces a strongly continuous group action on the underlying function space. In fact, G may act discontinuously. The results are applied to bifurcations of stable patterns arising in reaction-diffusion systems on the plane or in three-space modeling chemical systems such as catalysis on platinum surfaces and Belousov-Zhabotinsky reactions. These systems are equivariant under the Euclidean symmetry group. Hopf bifurcations from rigidly-rotating spiral waves to meandering or drifting waves and from twisted scroll rings are investigated.

Original languageEnglish (US)
Pages (from-to)122-149
Number of pages28
JournalJournal of Differential Equations
Volume141
Issue number1
DOIs
StatePublished - Nov 20 1997

Bibliographical note

Funding Information:
B. Sandstede was partially supported by a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation.

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