Propagating structures in globally coupled systems with time delays

We consider an ensemble of globally coupled phase oscillators whose interac tion is transmitted at finite speed. This introduces time delays, which mak e the spatial coordinates relevant in spite of the infinite range of the in teraction. In the limit of short delays, we show that the ensemble approach es a state of frequency synchronization, where all the oscillators have the same frequency, and can develop a nontrivial distribution of phases over s pace. Numerical calculations on one-dimensional arrays with periodic bounda ry conditions reveal that, in such geometry, the phase distribution is a pr opagating structure.