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We investigate phase-locked solutions of a continuum field of nonlocallycoupled identical phase oscillators with distance-dependent propagation delays.Equilibrium relations for both synchronous and traveling wave solutions in theparameter space characterizing the non-locality and time delay are delineated.For the synchronous states a comprehensive stability diagram is presented thatprovides a heuristic synchronization condition as well as an analytic relationfor the marginal stability curve. The relation yields simple stabilityexpressions in the limiting cases of local and global coupling of the phaseoscillators.

Phase locked solutions and their stability in the presence of propagation delays