• Open Access

Stable and unstable vortex knots in excitable media

Jack Binysh, Carl A. Whitfield, and Gareth P. Alexander
Phys. Rev. E 99, 012211 – Published 16 January 2019

Abstract

We study the dynamics of knotted vortices in a bulk excitable medium using the FitzHugh-Nagumo model. From a systematic survey of all knots of at most eight crossings we establish that the generic behavior is of unsteady, irregular dynamics, with prolonged periods of expansion of parts of the vortex. The mechanism for the length expansion is a long-range “wave-slapping” interaction, analogous to that responsible for the annihilation of small vortex rings by larger ones. We also show that there are stable vortex geometries for certain knots; in addition to the unknot, trefoil, and figure-eight knots reported previously, we have found stable examples of the Whitehead link and 62 knot. We give a thorough characterization of their geometry and steady-state motion. For the unknot, trefoil, and figure-eight knots we greatly expand previous evidence that FitzHugh-Nagumo dynamics untangles initially complex geometries while preserving topology.

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  • Received 12 September 2018

DOI:https://doi.org/10.1103/PhysRevE.99.012211

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary Physics

Authors & Affiliations

Jack Binysh1, Carl A. Whitfield2, and Gareth P. Alexander3,*

  • 1Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 2Division of Infection, Immunity and Respiratory Medicine, University of Manchester, Southmoor Road, Manchester M23 9LT, United Kingdom
  • 3Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom

  • *Corresponding author: G.P.Alexander@warwick.ac.uk

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Vol. 99, Iss. 1 — January 2019

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