Adaptive synchronization of weighted complex dynamical networks through pinning
State Key Laboratory of Industrial Control Technology, Institute of Industrial Control, Zhejiang University, Hangzhou, 310027, P.R. China
2 College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310032, P.R. China
Revised: 23 October 2007
Published online: 29 February 2008
This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.45.Xt – Synchronization; coupled oscillators / 89.75.-k – Complex systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008