Coupling Weight Matrix Design With Application to Network Synchronization: Proposals and Criterion

Synchronization for complex networks is investigated by designing appropriate coupling weight matrix. Coupling weight matrix design schemes are developed by using the properties of eigenvector and eigenvalue, which not only can ensure that the second largest eigenvalue of coupling weight matrix is not greater than any given negative constant but also the sum of off-diagonal elements of coupling weight matrix is the smallest. Furthermore, a sufficient condition about the second largest eigenvalue of the coupling weight matrix is presented to ensure the synchronization for complex networks and a numerical example verify the effectiveness of the coupling weight matrix design schemes.