Epicyclic drifting in anisotropic excitable media with multiple inhomogeneities: a dynamical system approach

The spiral is one of Natures more ubiquitous shape: it can be seen in various media, from galactic geometry to cardiac tissue. Spirals have been studied from a dynamical system perspective starting with Barkley’s seminal papers linking a wide class of spiral wave dynamics to the Euclidean symmetry of the excitable media in which they are observed [1,2]. But physical processes are never perfectly Euclidean: LeBlanc and Wulff introduced forced Euclidean symmetry-breaking (FESB) to the picture in order to give an explanation for phenomena (such as spiral anchoring and epicyclic drifting) that could not be understood within Barkleys framework alone [18, 19]. In previous articles, we studied spiral anchoring when symmetry-breaking takes the form of n simultaneous translational symmetry-breaking terms, with n > 1 [8] and when it takes the form of combined RSB and TSB terms [7]. In the same context, we now turn our attention to epicyclic drifting and integral (solution) manifolds of the perturbed center bundle equations derived in [7, 8]. AMS classification scheme numbers: 34C20, 37G40, 37L10, 37N25, 92E20 Submitted to: Journal of Differential Equations ‡ Present address: Institute of the Environment, University of Ottawa, Ottawa K1N 6N5, Canada. Epicyclic drifting in anisotropic media with multiple inhomogeneities 2