Pattern formation of coupled spiral waves in bilayer systems: rich dynamics and high-frequency dominance.

The interaction of two spiral waves with independent frequencies in a bilayer oscillatory medium (one spiral in each layer) and with a symmetric coupling e is studied. If the spirals have different frequencies, the faster spiral is unaffected by the slower one, and the slower can show a variety of behaviors, which depend on e and include, in order of increasing e, phase drifting, amplitude modulation, amplitude domination, and phase synchronization. This high-frequency dominance, the asymmetric driving-response effect under the condition of a symmetric coupling, is generic and independent of whether the coupled spiral waves are outwardly rotating or inwardly rotating spirals. If the spirals have identical frequencies, they may even show complete synchronization, parallel drift, or circular drift, depending on the relative rotation direction of the two spirals and their initial separation distance. Comparisons with coupled spirals in monolayer media, previous works on coupled spirals in bilayer systems, and coupled phase oscillators are made.