title: Persistent tangled vortex rings in generic excitable media.
abstract: Excitable media are exemplified by a range of living systems, such as mammalian heart muscle and its cells and Xenopus eggs. They also occur in non-living systems such as the autocatalytic Belousov-Zhabotinsky reaction. In most of these systems, activity patterns, such as concentration waves, typically radiate as spiral waves from a vortex of excitation created by some nonuniform stimulus. In three-dimensional systems, the vortex is commonly a line, and these vortex lines can form linked and knotted rings which contract into compact, particle-like bundles. In most previous work these stable 'organizing centres' have been found to be symmetrical and can be classified topologically. Here I show through numerical studies of a generic excitable medium that the more general configuration of vortex lines is a turbulent tangle, which is robust against changes in the parameters of the system or perturbations to it. In view of their stability, I suggest that these turbulent tangles should be observable in any of the many known excitable media.
authors.affiliation: Department of Ecology and Evolutionary Biology, University of Arizona, Tucson 85721.
authors.forename: A T
authors.initials: AT
authors.lastname: Winfree
mesh_terms: D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D009206:Myocardium; D014981:Xenopus