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Synchronization of complex dynamical networks with nonidentical nodes. (English) Zbl 1234.05218

Summary: This Letter investigates the synchronization problem of a complex network with nonidentical nodes, and proposes two effective control schemes to synchronize the network onto any smooth goal dynamics. By applying open-loop control to all nodes and placing adaptive feedback injections on a small fraction of network nodes, a low-dimensional sufficient condition is derived to guarantee the global synchronization of the complex network with nonidentical nodes. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network composed of nonidentical nodes, and an upper bound of impulsive intervals is estimated to ensure the global stability of the synchronization process. Numerical simulations are given to verify the theoretical results.

MSC:

05C82 Small world graphs, complex networks (graph-theoretic aspects)
34D06 Synchronization of solutions to ordinary differential equations
34B45 Boundary value problems on graphs and networks for ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
93C40 Adaptive control/observation systems
49N25 Impulsive optimal control problems
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