Propagating structures in globally coupled systems with time delays

We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. In the limit of short delays, we show that the ensemble approaches a state of frequency synchronization, where all the oscillators have the same frequency, and can develop a nontrivial distribution of phases over space. Numerical calculations on one-dimensional arrays with periodic boundary conditions reveal that, in such geometry, the phase distribution is a propagating structure.