Frequency clustering of coupled phase oscillators on small-world networks

We analyze the phenomenon of frequency clustering in a system ofcoupled phase oscillators. The oscillators, which in the absenceof coupling have uniformly distributed natural frequencies, arecoupled through a small-world network, built according to theWatts-Strogatz model. We study the time evolution and determinevariations in the transient times depending on the disorder ofthe network and on the coupling strength. We investigate theeffects of fluctuations in the average frequencies, and discussthe definition of the threshold for synchronization. Wecharacterize the structure of clusters and the distribution ofcluster sizes in the synchronization transition, and definesuitable order parameters to describe the aggregation of theoscillators as the network disorder and the coupling strengthchange. The non-monotonic behavior observed in some orderparameters is related to fluctuations in the mean frequencies.