Chemical oscillators on star graphs, theory and experiment

Oscillator networks represent a large class of physical systems in both the natural and engineered worlds. Here we present experimental data for chemical oscillators on star graphs with inhibitory coupling. We examine dynamics as a function of star-degree (number of nodes coupled to a central hub) and coupling strength. We control both by loading a water-in-oil Belousov-Zhabotinsky emulsion (drops ∼100μm) into etched-Si wafer wells. We observed three dynamical attractors: (1) a phase locked state in which the arm-nodes form a synchronized cluster, (2) center-silent dynamics in which the hub well is inhibited by the arm nodes and (3) unlocked dynamics. We developed theory at two levels: a chemically realistic discrete reaction-diffusion model and a phase model; we found excellent agreement to experiment. In particular, in the locked state, we find non-trivial dependence of the locking angle between the arm nodes and the hub as a function of star degree. Finally, we demonstrate that the system can be dynamically reconfigured through photo-inhibition of targeted drops.