Hypermeander of spirals: local bifurcations and statistical properties
University of Exeter; University of Houston; University of Surrey
In both experimental studies and numerical simulations of waves in excitable 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 review a number of recent results on dynamics with noncompact group symmetries and make the case that hypermeander may occur at a codimension two bifurcation from a rigidly rotating spiralwave.Our predictions are based on center bundle reduction (Sandstede, Scheel and Wulff), and on central limit theorems and invariance principles for group extensions of hyperbolic dynamical systems. These predictions are confirmed by numerical simulations of the center bundle equations.
Copyright © 2001 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 156, Issues 3-4, 2001, DOI: 10.1016/S0167-2789(01)00296-2
156 (3-4), pp. 364-382