  We study the synchronization phenomena in a system of globally coupled
oscillators with time delay in the coupling. The self-consistency equations for
the order parameter are derived, which depend explicitly on the amount of
delay. Analysis of these equations reveals that the system in general exhibits
discontinuous transitions in addition to the usual continuous transition,
between the incoherent state and a multitude of coherent states with different
synchronization frequencies. In particular, the phase diagram is obtained on
the plane of the coupling strength and the delay time, and ubiquity of
multistability as well as suppression of the synchronization frequency is
manifested. Numerical simulations are also performed to give consistent
results.
