Synchronization efficiency in coupled stochastic oscillators: The role of connection topology

We study the efficiency of synchronization in ensembles of identical coupled stochastic oscillator systems. By deriving a chemical Langevin equation, we measure the rate at which the systems synchronize. The rate at which the difference in the Hilbert phases of the systems evolve provides a suitable order parameter, and a 2--dimensional recurrence plot further facilitates the analysis of stochastic synchrony. We find that a global mean--field coupling effects the most rapid approach to global synchrony, and that when the number of "information carrying" molecular species increases, the rate of synchrony increases. The Langevin analysis is complemented by numerical simulations.