Research On Pinning Synchronozation Of Complex Dynamical Networks

The last decades have eyewitnessed the birth of a new movement of research interest in the study of complex networks. Research on them is pervading almost all disciplines of sciences today, incontrol science, information technology, physics, sociology, econonics, etc. In this paper, combining the nonliner system theory, control theory, algebraic graph theory and matrix analysis, the synchronization of complex dynamical networks is investigated systematically. The main work can be summarized as follows:There exist some fundamental and yet challenging problems in pinning synchroni-zation of complex networks:(1) What types of pinning schemes may be chosen for a given complex to realize synchronization? (2) What kinds of controllers may be chosen to ensure the network synchronization? (3) How large should the couping strength be used in a given complex network to achieve synchronization? There is large different from the complex network without delay because of the existing of delay. The complex network without delay must be synchronization if and only if the coupling strength is large enough. But for the complex network with delay existing in the node coupling, there exists optimum interval in the overall coupling strength ensuring the stability, which provides the important theoretical foundation for the study of anti-synchronization.The synchronization of complex dynamical networks with time-varying delay in both continuous and discrete time domains are controlled by applying local feedback injections to a small fraction of nodes in the whole network. The systems of the network are linearizedm on the equilibrium point, the problem of the the N×m-dimensional system is converted into the problem of the N independent m-dimensional linear systems. By some transformation, the synchronization problem of the complex network is transferred equally into the asymptotical stability problem. Then, considering the delay existing in the node coupling, the problem of synchronization problem is converted to validating the linear matrix inequalities(LMIs).