Wang, Yangling; Cao, Jinde Cluster synchronization in nonlinearly coupled delayed networks of non-identical dynamic systems. (English) Zbl 1254.93013 Nonlinear Anal., Real World Appl. 14, No. 1, 842-851 (2013). 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. Cited in 42 Documents 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 Keywords:cluster synchronization; pinning control; nonlinearly coupled networks; time-varying delay; non-identical dynamic systems PDF BibTeX XML Cite \textit{Y. Wang} and \textit{J. Cao}, Nonlinear Anal., Real World Appl. 14, No. 1, 842--851 (2013; Zbl 1254.93013) Full Text: DOI OpenURL