Synchronization criterion of complex networks with time-delay under mixed topologies

Abstract Two kinds of synchronization issues are studied in this paper. First, the synchronization problems of complex network with time-delay are investigated using pinning control. A type of original mixed topologies with time-delay is proposed, which contains directed networks and undirected networks. The pinning controllers are constructed to make the networks synchronization. Second, the synchronization problems between two different complex dynamical networks with time-delay are investigated using Taylor expansion. The two different complex networks have various topological structures. Finally, simulation examples illustrate that the theoretical methods are effective.

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