Meandering and drifting spiral waves has been observed in many experiments, and also in numerical simulations of reaction-diffusion systems. Numerical evidence shows that these spiral waves can be created in Hopf bifurcations of rigidly-rotating spiral waves. Barkley explained the transition from meandering to drifting as a resoncance phenomenon which involves the Euclidean symmetry group of the plane. In this talk, a geometric center-manifold approach is presented which corroborates Barkley's conclusions. In fact, it allows us to describe bifurcations of spiral waves by finite-dimensional ODEs. Some examples of such bifurcations are given. Finally, the limitations of our result are explained. This is joint work with B. Fiedler, A. Scheel and C. Wulff.

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