Novel type of amplitude spiral wave in a two-layer system

Interaction of spiral waves in a two-layer system described by a model of coupled complex Ginzburg–Landau equations with negative-feedback couplings e1 and e2 is studied. Synchronization of two spiral waves can be broadly found if e1+e2 is sufficiently large. Prior to the synchronization, under the condition of strongly asymmetric coupling (|e1−e2|⪢0), a novel type of spiral wave, amplitude spiral wave, exists in the driven system. The pattern of amplitude spiral wave shows the spiral in the amplitude and without a singularity point (tip), compared to usual spiral waves known for phase with amplitude uniform far away from tips and rotating around tips.