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Nonlinear Dynamics

, Volume 53, Issue 1–2, pp 107–115 | Cite as

Adaptive synchronization of uncertain dynamical networks with delayed coupling

  • Jianquan Lu
  • Jinde Cao
Original Paper

Abstract

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 η 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.

Keywords

Adaptive synchronization Complex networks Time delay 

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingChina
  2. 2.Department of MathematicsCity University of Hong KongHong KongChina

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