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Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling. (English) Zbl 1225.05223
Summary: This Letter investigates the global synchronization of a general complex dynamical network with non-delayed and delayed coupling. Based on Lasalle’s invariance principle, adaptive global synchronization criteria is obtained. Analytical result shows that under the designed adaptive controllers, a general complex dynamical network with non-delayed and delayed coupling can globally asymptotically synchronize to a given trajectory. What is more, the node dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition and the coupling matrix is not assumed to be symmetric or irreducible. Finally, numerical simulations are presented to verify the effectiveness of the proposed synchronization criteria.

05C82Small world graphs, complex networks (graph theory)
34B45Boundary value problems for ODE on graphs and networks
34H10Chaos control (ODE)
93C40Adaptive control systems
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