  We develop a renormalization group method to investigate synchronization
clusters in a one-dimensional chain of nearest-neighbor coupled phase
oscillators. The method is best suited for chains with strong disorder in the
intrinsic frequencies and coupling strengths. The results are compared with
numerical simulations of the chain dynamics and good agreement in several
characteristics is found. We apply the renormalization group and simulations to
Lorentzian distributions of intrinsic frequencies and couplings and investigate
the statistics of the resultant cluster sizes and frequencies, as well as the
dependence of the characteristic cluster length upon parameters of these
Lorentzian distributions.
