  A modified Kuramoto model of synchronization in a finite discrete system of
locally coupled oscillators is studied. The model consists of N oscillators
with random natural frequencies arranged on a ring. It is shown analytically
and numerically that finite-size systems may have many different synchronized
stable solutions which are characterised by different values of the winding
number. The lower bound for the critical coupling is given, as well as an
algorithm for its exact calculation. It is shown that in general phase-locking
does not lead to phase coherence in 1D.
