Analyzing and controlling the network synchronization regions

In this paper, the commonly concerned issue of synchronization regions of complex dynamical networks is investigated, for the case when the synchronous state is an equilibrium point. Some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form (-∞,α1) are established, where α1 is a constant. In addition, a sufficient condition for the existence of a bounded synchronization region of the form (α2,α3) is derived, where α2 and α3 are constants, by using the parameter-dependent Lyapunov function method. Furthermore, some effective controller design methods are presented that can change the synchronization regions, thereby managing the synchronizability of the network. Finally, some numerical examples are given to show that a dynamical network may have disconnected synchronization regions, particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of (-∞,α1)∪(α2,α3).