Phase correlation and clustering of a nearest neighbour coupled oscillators system

We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time-average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied.