Synchronization Enhance on Scale-Free Network

Many real networks have been found to have a rich degree of symmetry, which is a universal structural property of network, we investigate the synchronization property of oscillators on symmetry network. One of fascinating problems related to symmetry network is how to enhance phase synchronization under symmetry structure. For this purpose, statistics the orbits of automorphism groups of the symmetry network, the nodes in the same orbit have similar or equivalent properties, then we optimization the network topology structure by symmetry properties of network. The size of the optimization network is determined by the richness of symmetry in the network topology, the more symmetric the network is, the smaller the size of the new network is. The phase synchronization of the different orbits, the optimized networks and the original networks of BA by simulated. Analysis of these simulations shows that symmetry structure can enhance phase synchronization of network.