Synchronization of Phase-coupled Oscillators with Distance-dependent Delay

By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the nodes on a square lattice while introducing finite interaction velocity, which gives rise to non-uniform delay. It is found that such delay facilitates incoherence and removes reentrant behavior found in models with uniform delay. A coupling-delay phase diagram is obtained and compared with previous results for uniform delay.