Local and Global Synchronization Criteria for a Generalized Complex Dynamical Network Model

This paper investigates the local and global synchronization of a generalized complex dynamical network model with constant and delayed coupling. The uncoupled dynamical behavior at each node is general, and can be chaotic or otherwise. By constructing a new class of Lyapunov functionals combined with free-weighting matrices, a less conservative criterion ensuring delay-dependent synchronization is derived in terms of linear matrix inequalities(LMIs). Furthermore, the sufficient condition for the global synchronization of the generalized network is obtained. A prototype composed of the chaotic Duffing oscillators is discussed to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.