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Outer synchronization of complex networks with nondelayed and time-varying delayed couplings via pinning control or impulsive control. (English) Zbl 1342.93017

Summary: The outer synchronization problem between two complex networks with nondelayed and time-varying delayed couplings via two different control schemes, namely, pinning control and impulsive control, is considered. Firstly, by applying pinning control to a fraction of the network nodes and using a suitable Lyapunov function, we obtain some new and useful synchronization criteria, which guarantee the outer synchronization between two complex networks. Secondly, impulsive control is added to the nodes of corresponding response network. Based on the generalized inequality about time-varying delayed different equation, sufficient conditions for outer synchronization are derived. Finally, some examples are presented to demonstrate the effectiveness and feasibility of the results obtained in this paper.

MSC:

93A15 Large-scale systems
93A14 Decentralized systems
93D30 Lyapunov and storage functions
93C15 Control/observation systems governed by ordinary differential equations
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