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Zbl 1182.92007
Lu, Jianquan; Cao, Jinde
Adaptive synchronization of uncertain dynamical networks with delayed coupling. (English)
[J] Nonlinear Dyn. 53, No. 1-2, 107-115 (2008). ISSN 0924-090X; ISSN 1573-269X/e

Summary: We propose a simple scheme for the synchronization of an uncertain complex dynamical network with delayed coupling. Based on the Lyapunov stability theory of functional differential equations, certain controllers can be designed for ensuring the states of uncertain dynamical network with coupling delays to globally asymptotically synchronize by combining the adaptive method and linear feedback with the updated feedback strength. Different update gains $\eta i$ will lead to different rates toward synchrony, the choice of which depends on the concrete systems and network models. This strategy can be applied to any complex dynamical network (regular, small-world, scale-free or random). Numerical examples with respectively nearest-neighbor coupling and scale-free structure are given to demonstrate the effectiveness of our presented scheme.

MSC 2000:: *92B20 General theory of neural networks
34K20 Stability theory of functional-differential equations
34K60 Applications of functional-differential equations

Keywords: adaptive synchronization; complex networks; time delay

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