Rotational synchronization of pinned spiral waves

Coupled rotors can spontaneously synchronize, giving rise to a plethora of intriguing dynamics. We present here a pair of spiral waves as two synchronizing rotors, coupled by diffusion. The spirals are pinned to unexcitable obstacles, which enables us to modify their frequencies and restrain their drift. In experiments with the Belousov-Zhabotinsky reaction, we show that two counterrotating spiral rotors, pinned to circular hetero-geneities, can synchronize in frequency and phase. The nature of the phase synchronization varies depending on the difference in their characteristic frequencies. We observe in-phase and out-of-phase synchronization, lag synchronization, and phase resetting across the experiments. The time required for the two spirals to synchronize is found to depend upon the relative size of their pinning obstacles and the distance separating them. This distance can also modify the phase lag of the two rotors upon synchronization. Our experimental observations are reproduced and explained further on the basis of numerical simulations of an excitable reaction-diffusion model.

Automated summary

This study demonstrates the synchronization of coupled rotors, specifically two spiral waves, using diffusion as the coupling mechanism. The frequency and phase synchronization of the spiral waves can be modified by pinning them to unexcitable obstacles. Experimental results show different types of phase synchronization depending on the difference in characteristic frequencies of the rotors. The time required for synchronization and the phase lag between the rotors can be influenced by the relative size of the pinning obstacles and the distance between the rotors.