  Re-entrant spiral waves are observed in many different situations in nature,
perhaps most importantly in excitable electrophysiological tissue where they
are believed to be responsible for pathological conditions such as cardiac
arrhythmias, epileptic seizures and hallucinations. Mathematically, spiral
waves occur as solutions to systems of reaction-diffusion partial differential
equations (RDPDEs) which are frequently used as models for electrophysiological
phenomena. Because of the invariance of these RDPDEs with respect to the
Euclidean group SE(2) of planar translations and rotations, much progress has
been made in understanding the dynamics and bifurcations of spiral waves using
the theory of group-equivariant dynamical systems. In reality however,
Euclidean symmetry is at best an approximation. Inhomogeneities and anisotropy
in the medium of propagation of the waves break the Euclidean symmetry, and can
lead to such phenomena as anchoring and drifting. In this paper, we study the
effects on quasi-periodic meandering spiral waves of a small perturbation which
breaks the continuous SE(2) symmetry, but preserves the symmetry of a regular
square lattice.
