Transition from non-synchronization to synchronization of complex networks

A novel measure to describe the transition of the network from non-synchronization to synchronization is proposed. Based on a scale-free network with non-symmetric and weighted coupling, the transition of the network from non-synchronization to synchronization becomes fastest for appropriate non-symmetric coupling. Moreover, the minimal coupling cost of the network with non-symmetric and weighted coupling may be reduced significantly as compared to the case of symmetric and unweighted coupling.