Patterns of phase-dependent spiral wave attenuation in excitable media

We show that introducing periodic planar fronts with long excitation duration can lead to spiral attenuation. The attenuation occurs periodically over cycles of several planar fronts, forming a variety of complex spatiotemporal patterns. We find that these attenuation patterns occur only at specific phases of the descending fronts relative to the rotational phase of the spiral. These patterns fall into two general classes, each defined by a specific expression for the number of attenuated spirals per cycle of planar fronts, and represented by a structured diagram in parameter space. The spiral attenuation patterns we observe remain stable in time and do not change during the evolution of the system.