Synchronization of the Kuramoto model with multi-scale-free property

The synchronizability of a general Kuramoto model is studied in this paper. A lower bound of the critical coupling strength is provided, which shows that the synchronization of the Kuramoto model depends on not only its network structure, but the distribution of nodes natural frequency. When these properties follow scale-free distributions, we find that the homogeneous networks are more synchronizable than heterogeneous ones.