WIAS Preprint No. 288, (1996)

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


  • Sandstede, Björn
  • Scheel, Arnd
  • Wulff, Claudia

2010 Mathematics Subject Classification

  • 35B32 35K57 57S20 57S30


  • spiral waves, non-compact groups, center manifolds, Hopf bifurcation




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.

Appeared in

  • J. Differential Equations, 141 (1997), pp. 122-149

Download Documents