Effects of coupling-frequency correlations on synchronization of complete graphs

We introduce a model to study the effects of coupling-frequency correlations on synchronization in complete graphs. When the linear correlation is adopted, we find a symmetric network where frequencies of the oscillators are distributed in a bipolar way, having values either −1 or +1. In the network, the oscillators either all drift or all phase-locked. The behavior can separate qualitatively two other types of correlations, where slow and fast oscillators can remain unsynchronized respectively. It is obvious that the weighting exponent plays an important role. Besides, the numerical simulation results indicate that the linear correlation has the best performance in synchronization ability among three types of correlations in view of the average node cost.