Synchronization Transitions in a Disordered Josephson Series Array

We show that a current-biased series array of nonidentical Josephson junctions undergoes two transitions as a function of the spread of natural frequencies. One transition corresponds to the onset of partial synchronization, and the other corresponds to complete phase locking. In the limit of weak coupling and disorder, the system can be mapped onto an exactly solvable model introduced by Kuramoto and the transition points can be accurately predicted.