  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.

Pattern Formation and Solitons;Soft Condensed Matter;High Energy Physics - Theory;Fluid Dynamics