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Persistent tangled vortex rings in generic excitable media

Nature volume 371, pages 233–236 (1994)Cite this article

Abstract

EXCITABLE media are exemplified by a range of living systems1–8, such as mammalian heart muscle6 and its cells1 and Xenopus eggs2,3. They also occur in non-living systems such as the autocatalytic Belousov–Zhabotinsky reaction9–14. In most of these systems, activity patterns, such as concentration waves, typically radiate as spiral waves from a vortex of excitation created by some non-uniform 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 bundles9–30. 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.

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  1. Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, Arizona, 85721, USA

    A. T. Winfree

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Winfree, A. Persistent tangled vortex rings in generic excitable media. Nature 371, 233–236 (1994). https://doi.org/10.1038/371233a0

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