Topologically Mismatched Pinning of Scroll Waves

Abstract

Three-dimensional scroll waves in excitable reaction−diffusion systems rotate around one-dimensional phase singularities. Although these filaments are dynamic objects, their motion can be arrested if pinned to unexcitable obstacles. We study this vortex pinning for a case in which the topology of the initial filament (circular loop) differs from the topology of the obstacle (double torus). In experiments with the Belousov−Zhabotinsky reaction and numerical simulations, we show that pinning is possible and that it induces periodic rotation patterns. Continuous rotation extends around either one or both halves of the double torus. The latter case is doubly degenerate because waves can move through the two holes in the same or opposite directions. Opposite rotation is organized by a two-armed vortex segment that emits waves at a period approximately two-times larger than the other pinned vortex states.