THE OPTIMUM OF SYNCHRONIZABILITY IN COMPLEX NETWORKS
PEI-JIE MA, Bing-Hong Wang · International Journal of Modern Physics C · 2010
In this brief report, we investigate the synchronizability of the complex network. In order to optimize the synchronizability, we propose a method by introducing a weight matrix, which makes the synchronized states stable for the widest range of the overall coupling strength. We give a proof in mathematics and gain the exact form of the weight matrix, which is equal to Lβ. Matrix L is the one that describes the optimal network and matrix β is constructed by the eigenvalues and eigenvectors of the usual Laplacian matrix. This result may provide us insight into the synchronization of complex network more deeply.