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Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems. (English) Zbl 1254.93013

Summary: In the real world, many networks show community structure, i.e., clusters of nodes, which have a high density of links within the same cluster but a lower density of links between different clusters. In this paper, nonlinearly coupled networks with community structure and non-identical nodes and with time-varying delay are considered. By applying pinning control to a fraction of network nodes, and using a suitable Lyapunov function, we obtain some new and useful synchronization criteria, which guarantee that various clusters are synchronized independently. An example is presented to show the application of the criteria obtained in this paper.

MSC:

93A15 Large-scale systems
93C95 Application models in control theory
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
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