Abstract
This paper considers synchronization problems in networks of chaotic systems with time-delayed couplings. First of all, we show that synchronization patterns can be estimated from eigenvectors of the graph Laplacian related to the scaling method for synchronization conditions. Then, we consider synchronization in Cartesian product networks. By combining the proposed estimation method with the properties of the Cartesian product, we can easily detect synchronization patterns emerging in the Cartesian product networks from the eigenvalues of the original networks. Some numerical examples are provided to demonstrate the validity of the proposed estimation method.
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