Hypermeander of spirals: local bifurcations and statistical properties

In both experimental studies and numerical simulations of waves in excitabl e media, rigidly rotating spiral waves are observed to undergo transitions to complicated spatial dynamics with long-term Brownian-like motion of the spiral tip. This phenomenon is known as hypermeander. In this paper, we rev iew a number of recent results on dynamics with noncompact group symmetries and make the case that hypermeander may occur at a codimension two bifurca tion from a rigidly rotating spiral wave. Our predictions are based on cent er bundle reduction (Sandstede, Scheel and Wulff), and on central limit the orems and invariance principles for group extensions of hyperbolic dynamica l systems. These predictions are confirmed by numerical simulations of the center bundle equations. (C) 2001 Published by Elsevier Science B.V.