Hypermeander of spirals: local bifurcations and statistical properties
Ashwin, Peter; Melbourne, Ian; Nicol, Matthew
Date: 25 July 2001
Journal
Physica D
Publisher
Elsevier
Publisher DOI
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 ...
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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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