  Driven by various kinds of noise, ensembles of limit cycle oscillators can
synchronize. In this letter, we propose a general formulation of
synchronization of the oscillator ensembles driven by common colored noise with
an arbitrary power spectrum. To explore statistical properties of such colored
noise-induced synchronization, we derive the stationary distribution of the
phase difference between two oscillators in the ensemble. This analytical
result theoretically predicts various synchronized and clustered states induced
by colored noise and also clarifies that these phenomena have a different
synchronization mechanism from the case of white noise.
