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Dynamics of linked filaments in excitable media

Maucher, Fabian; Sutcliffe, Paul

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Fabian Maucher


In this paper we present the results of parallel numerical computations of the long-term dynamics of linked vortex filaments in a three-dimensional FitzHugh–Nagumo excitable medium. In particular, we study all torus links with no more than 12 crossings and identify a timescale over which the dynamics is regular in the sense that each link is well-described by a spinning rigid conformation of fixed size that propagates at constant speed along the axis of rotation. We compute the properties of these links and demonstrate that they have a simple dependence on the crossing number of the link for a fixed number of link components. Furthermore, we find that instabilities that exist over longer timescales in the bulk can be removed by boundary interactions that yield stable torus links which settle snugly at the medium boundary. The Borromean rings are used as an example of a non-torus link to demonstrate both the irregular tumbling dynamics that arises in the bulk and its suppression by a tight confining medium. Finally, we investigate the collision of torus links and reveal that this produces a complicated wrestling motion where one torus link can eventually dominate over the other by pushing it into the boundary of the medium.


Maucher, F., & Sutcliffe, P. (2019). Dynamics of linked filaments in excitable media. Nonlinearity, 32(3), Article 942.

Journal Article Type Article
Acceptance Date Jan 3, 2019
Online Publication Date Feb 13, 2019
Publication Date Feb 13, 2019
Deposit Date Feb 25, 2019
Publicly Available Date Feb 13, 2020
Journal Nonlinearity
Print ISSN 0951-7715
Electronic ISSN 1361-6544
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 32
Issue 3
Article Number 942


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