Spiral Anchoring in Media with Multiple Inhomogeneities: A Dynamical System Approach

The spiral is one of Nature’s more ubiquitous shape: it can be seen in various media, from galactic geometry to cardiac tissue. In the literature, very specific models are used to explain some of the observed incarnations of these dynamic entities. Barkley [1, 2] first noticed that the range of possible spiral behaviour is caused by the Euclidean symmetry that these models possess. In experiments however, the physical domain is never perfectly Euclidean. The heart, for instance, is finite, anisotropic and littered with inhomogeneities. To capture this loss of symmetry (and as a result model the physical situation with a higher degree of accuracy), LeBlanc and Wulff introduced forced Euclidean symmetry-breaking (FESB) in the analysis, via two basic types of perturbations: translational symmetrybreaking (TSB) and rotational symmetry-breaking terms. In [3, 4], they show that phenomena such as anchoring and quasi-periodic meandering can be explained by combining Barkley’s insight with FESB. In this article, we provide a fuller characterization of spiral anchoring by studying the effects of n simultaneous TSB perturbations, where n > 1. AMS classification scheme numbers: 34C20, 37G40, 37L10, 37N25, 92E20 Submitted to: Journal of Nonlinear Science ‡ Present address: Institute of the Environment, University of Ottawa, Ottawa K1N 6N5, Canada. Spiral anchoring in media with multiple inhomogeneities 2