Synchronization Patterns in Network-of-Networks of Chaotic Systems via Cartesian Product*

This paper considers the synchronization problem in network-of-networks of chaotic systems with time-delay. We have already proposed an estimation method for full/partial synchronization conditions for networks of chaotic systems via the Cartesian product. In this paper, we attempt to estimate full/partial synchronization conditions for the Cartesian product networks with time-delay by using the scaling method for synchronization condition and the properties of the Cartesian product. The validity of the estimation method is tested through a numerical example.