On synchronized regions of discrete-time complex dynamical networks

In this paper, the local synchronization of discrete-time complex networks is studied. First, it is shown that for any natural number n, there exists a discrete-time network which has at least disconnected synchronized regions for local synchronization, which implies the possibility of intermittent synchronization behaviors. Different from the continuous-time networks, the existence of an unbounded synchronized region is impossible for discrete-time networks. The convexity of the synchronized regions is also characterized based on the stability of a class of matrix pencils, which is useful for enlarging the stability region so as to improve the network synchronizability.