Nonlocal Synchronization in Nearest Neighbor Coupled oscillators

We investigate a system of nearest neighbor coupled oscillators. We show that the nonlocal frequency synchronization, that might appear in such a system, occurs as a consequence of the nearest neighbor coupling. The power spectra of nonadjacent oscillators show that there is no complete coincidence between all frequency peaks of the oscillators in the nonlocal cluster, while the peaks for neighboring oscillators approximately coincide even if they are not yet in a cluster. It is shown that nonadjacent oscillators closer in frequencies, share slow modes with their adjacent oscillators which are neighbors in space. It is also shown that when a direct coupling between non-neighbors oscillators is introduced explicitly, the peaks of the spectra of the frequencies of those non-neighbors coincide.