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Talk Abstract
Meandering and Drifting of Spiral Waves

Institute for Mathematics and Its Applications
Bjorn Sandstede, Ohio State University

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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