Spiral anchoring in anisotropic media with multiple inhomogeneities: a dynamical system approach

Spirals abound in excitable media. Various PDE models have been suggested in order to explain and predict some of the incarnations of these dynamic entities. In two landmark papers, Barkley [1, 2] noticed that a general family of these were caused by the Euclidean symmetry (inherent in the media) of the models. But the experimental universe is un-perfectly Euclidean, by necessity. The heart, for instance, is finite, anisotropic and littered with inhomogeneities. LeBlanc and Wulff first introduced forced Euclidean symmetry-breaking (FESB) in the analysis, in the form of translational symmetry-breaking (TSB) perturbations [3] and rotational symmetry-breaking (RSB) perturbations [4]; in either case, it is shown that spiral anchoring is a direct consequence of the FESB. In [5], Boily, LeBlanc and Matsui studied the effects that n simultaneous TSB perturbations have on spiral anchoring. In this article, we provide a characterization of spiral anchoring in the presence of a combination of RSB and TSB perturbations. AMS classification scheme numbers: 34C20, 37G40, 37L10, 37N25, 92E20 Submitted to: Nonlinearity ‡ Present address: Institute of the Environment, University of Ottawa, Ottawa K1N 6N5, Canada. Spiral anchoring in anisotropic media with multiple inhomogeneities 2