Excitatory and inhibitory coupling in a one-dimensional array of Belousov-Zhabotinsky micro-oscillators: theory.

We study numerically the behavior of one-dimensional arrays of aqueous droplets containing the oscillatory Belousov-Zhabotinsky reaction. Droplets are separated by an oil phase that allows coupling between neighboring droplets via two species: an inhibitor, Br(2), and an activator, HBrO(2). Excitatory coupling alone (through the activator) generates in-phase oscillations and/or "waves," while inhibitory coupling alone (through Br(2)) gives rise to antiphase oscillations, Turing patterns, and their combinations. The simultaneous presence of excitatory and inhibitory coupling leads to a large number of new spatiotemporal patterns, including some that exhibit very complex behavior. Analysis of a simple model allows us to simulate patterns resembling those observed experimentally under similar conditions and to elucidate the contributions of droplet and gap sizes, activator and inhibitor partition coefficients, and malonic acid concentration to the coupling strengths.