The effect of time-delay on anomalous phase synchronization

Anomalous phase synchronization in nonidentical interacting oscillators is manifest as the increase of frequency disorder prior to synchronization. We show that this effect can be enhanced when a time-delay is included in the coupling. In systems of limit-cycle and chaotic oscillators we find that the regions of phase disorder and phase synchronization can be interwoven in the parameter space such that as a function of coupling or time-delay the system shows transitions from phase ordering to disorder and back.