Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators

The transition to phase synchronization in systems consisting of a large number (Formula presented) of coupled nonlinear oscillators via the route of phase clustering (phase synchronization among subsets of oscillators) is investigated. We elucidate the mechanism for the merger of phase clusters and find an algebraic scaling between the critical coupling parameter required for phase synchronization and N. Our result implies that, in realistic situations, phase clustering may be more prevalent than full phase synchronization.