Dynamics of Spiral Waves on Unbounded Domains Using Center-Manifold Reductions

An equivariant center-manifold reduction near relative equilibria ofG-equivariant semiflows on Banach spaces is presented. In contrast to previous results, the Lie groupGinduces a strongly continuous group action on the underlying function space. In fact,Gmay 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.