Synchronization patterns in geometrically frustrated rings of relaxation oscillators.

Diffusively coupled chemical oscillators can exhibit a wide variety of complex spatial patterns. In this paper, we show that a ring of relaxation oscillators diffusively coupled through the inhibitory species leads to remarkable spatiotemporal patterns in the regime where there is a large separation of time scales between the activator and the inhibitor dynamics. The origin of these complex patterns can be traced back to a preponderance of antiphase synchronized states in the space of attractors.

Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions.

Recent experiments in one- and two-dimensional microfluidic arrays of droplets containing Belousov-Zhabotinsky reactants show a rich variety of spatial patterns [M. Toiya et al., J.