Adaptive Synchronization on Edges of Complex Networks

This paper studies distributed adaptive control for synchronization on edges of complex networks. Some distributed adaptive strategies are designed on all the coupling weights of the network for reaching synchronization, which are then extended to the case where only a small fraction of coupling weights are adjusted. A general criterion is given and it is found that synchronization can be reached if the corresponding edges and nodes of the updated coupling weights form a spanning tree. Finally, simulation examples are given to illustrate the theoretical analysis.