Synchronization via superdiffusive mixing in an extended, advection-reaction-diffusion system

We study synchronization of the Belousov-Zhabotinsky (BZ) chemical reaction in an annular chain of alternating vortices. The vortex chain can (a) oscillate, in which case chaotic advection enhances mixing between adjacent vortices, and/or (b) drift, in which case a jet region forms allowing tracers to travel rapidly around the annulus. If the chain both oscillates and drifts, the long-range transport is diffusive for drift velocity $v_d <$ oscillation velocity $v_o$ and superdiffusive for $v_d > v_o$. We map out the regimes in parameter space ($v_o$ versus $v_d$) where the BZ reaction synchronizes. We find that synchronization is much more prevalent for the regimes in which transport is superdiffusive. The results are interpreted by considering Levy flights -- tracer trajectories characterized by long jumps -- associated with superdiffusive transport as ``short-cuts'' connecting distant parts of the system, similar to those proposed for discrete ``small world'' networks.