Spiral wave dynamics in oscillatory inhomogeneous media

The effect of a long length scale static inhomogeneity on spiral wave dynamics is studied in the two-dimensional complex Ginzburg-Landau equation. We find that the inhomogeneity leads to the formation of a dominant spiral domain that suppresses other spiral domains, and that the spiral vortices slowly drift in the presence of an inhomogeneity with a velocity that is proportional to the local parameter gradients. We derive an expression for the spiral vortex drift velocity and present examples of both fixed point and limit cycle attractors of the spiral vortices.