Disconnected Synchronized Regions of Complex Dynamical Networks

This technical note addresses the synchronized region problem, which is converted to a more convenient matrix stability problem, for complex dynamical networks. For any natural numbern, the existence of a network withndisconnected synchronized regions is theoretically proved and numerically demonstrated. This shows the intrinsic complexity of the network synchronization problem. Convexity characteristic of stability for relevant matrix pencils is further discussed. A smooth Chua's circuit network is finally discussed as an example for illustration.