Synchronization of Networked Systems and Laplacian-Spectrum Modification

In this paper, synchronization-related problems of networked systems are considered. Simple necessary conditions are given with help of the estimated bounds of the eigenvalues of the coupled Laplacian. These conditions are easy to check since we mainly choose maximum and minimum vertex degrees and other easily obtained network parameters. Moreover, the effects of adding/removing edges of the original network topology on synchronization is also considered. Suggestions about edge addition/removal to improve the synchronization situations in networked systems are given.