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Rotating spiral waves organize spatial patterns in chemical, physical andbiological excitable systems. Factors affecting their dynamics such asspatiotemporal drift are of great interest for par- ticular applications. Here,we propose a quantitative description for spiral wave dynamics on curvedsurfaces which shows that for a wide class of systems, including the BZreaction and anisotropic cardiac tissue, the Ricci curvature scalar of thesurface is the main determinant of spiral wave drift. The theory providesexplicit equations for spiral wave drift direction, drift velocity and theperiod of rotation. Depending on the parameters, the drift can be directed tothe regions of either maximal or minimal Ricci scalar curvature, which wasverified by direct numerical simulations.

Drift Laws for Spiral Waves on Curved Anisotropic Surfaces