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Zbl 1197.34092
Liu, Tao; Zhao, Jun; Hill, David J.
Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes. (English)
[J] Chaos Solitons Fractals 40, No. 3, 1506-1519 (2009). ISSN 0960-0779

Summary: We study the global synchronization of nonlinearly coupled complex delayed dynamical networks with both directed and undirected graphs. Via Lyapunov-Krasovskii stability theory and the network topology, we investigate the global synchronization of such networks. Under the assumption that coupling coefficients are known, a family of delay-independent decentralized nonlinear feedback controllers are designed to globally synchronize the networks. When coupling coefficients are unavailable, an adaptive mechanism is introduced to synthesize a family of delay-independent decentralized adaptive controllers which guarantee the global synchronization of the uncertain networks. Two numerical examples of directed and undirected delayed dynamical network are given, respectively, using the Lorenz system as the nodes of the networks, which demonstrate the effectiveness of proposed results. \par Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC 2000:: *34D06
34K20 Stability theory of functional-differential equations
37D45 Strange attractors, chaotic dynamics
37N35 Dynamical systems in control
93D15 Stabilization of systems by feedback
93D21 Adaptive and robust stabilization

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