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Synchronization of the Non-delayed and Delayed Coupling Complex Network Via Adaptive Controlling

This paper studies the synchronization of a general complex dynamical network with non-delayed and delayed coupling. What is more, the coupling matrix is not necessary sym- metric or irreducible. Adaptive controllers have been designed to make the dynamical network synchronize. Analytical results show that the states of the dynamical network with non-delayed and delayed coupling can globally asymptotically synchronize onto a desired orbit under the designed controllers. A numerical example is given to demonstrate the validity of the proposed method, in which the famous Lsystem is chosen as the node of the network.