Abstract
This paper considers the synchronization problem in networks of nonlinear systems with time-delayed couplings. We show that synchronization patterns can be estimated from eigenvectors of the graph Laplacian combined with the scaling method for synchronization conditions. Furthermore, we consider synchronization in large-scale networks created by taking a couple of graph products of networks. By combining the proposed estimation method with the properties of graph products, we can easily detect synchronization patterns emerging in the networks from the eigenvalues of the original networks. Some numerical examples illustrate the validity of the proposed estimation methods.
