  We study synchronization of sinusoidally coupled phase oscillators on
networks with modular structure and a large number of oscillators in each
community. Of particular interest is the hierarchy of local and global
synchrony, i.e., synchrony within and between communities, respectively. Using
the recent ansatz of Ott and Antonsen, we find that the degree of local
synchrony can be determined from a set of coupled low-dimensional equations. If
the number of communities in the network is large, a low-dimensional
description of global synchrony can be also found. Using these results, we
study bifurcations between different types of synchrony. We find that,
depending on the relative strength of local and global coupling, the transition
to synchrony in the network can be mediated by local or global effects.
