Physica D 156 (2001) 364-382
Peter Ashwin, Ian Melbourne and Matthew Nicol
Abstract
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 spiral wave. Our predictions are based on center bundle reduction (Sandstede, Scheel & Wulff), and on central limit theorems and invariance principles for noncompact group extensions of hyperbolic dynamical systems. These predictions are confirmed by numerical simulations of the center bundle equations.
The central limit theorems and invariance principles used in this paper are developed in Nicol, Melbourne & Ashwin and in Field, Melbourne & Torok