Abstract.
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)
S.S. Yang, C.K. Duan, Chaos, Solitons & Fractals 9, 1703 (1998)
H.U. Voss, Phys. Rev. E 61, 5115 (2000)
M.C. Ho, Y.C. Huang, Phys. Lett. A 301, 424 (2002)
Z.M. Ge, Y.S. Chen, Chaos, Solitons & Fractals 21, 101 (2004)
M.T. Yassen, Chaos, Solitons & Fractals 26, 913 (2005)
Coupled Map Lattices, edited by K. Kaneko (World Scientific, Singapore, 1992)
C.W. Wu, L.O. Chua, IEEE Trans. Circuits Syst. I 42, 430 (1995)
L.O. Chua, CNN: A Paradigm for complexity (World Scientific, Singapore, 1998)
H. Atmanspacher, T. Filk, H. Scheingraber. Eur. Phys. J. B 44, 229 (2005)
C. Peskin, Mathematical Aspects of Heart Physiology (Courant Inst. Math. Sci., New York, 1977)
Z. Neda, E. Ravasz, Y. Brechet, T. Vicsek, A.-L. Barabási, Nature (London) 403, 849 (2000)
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
D.J. Watts, S.H. Strogatz, Nature (London) 393, 440 (1998)
A.-L. Barabási, R. Albert, Science 86, 509 (1999)
R.O. Grigoriev, M.C. Cross, H.G. Schuster, Phys. Rev. Lett. 79, 2795 (1997)
N. Parekh, S. Parthasarathy, S. Sinha, Phys. Rev. Lett. 81, 1401 (1998)
X. Wang, G. Chen, Physica A 310, 521 (2002)
X. Li, X. Wang, G. Chen, IEEE Trans. Circuits Syst. I 51, 2074 (2004)
T. Chen, X. Liu, W. Lu, IEEE Trans. Circuits Syst. I 54, 1317 (2007)
F. Sorrentino, M. di Bernardo, F. Garofalo, G. Chen, Phys. Rev. E 75, 046103 (2007)
F. Sorrentino, Chaos 17, 033101 (2007)
J. Xiang, G. Chen, Automatica 43, 1049 (2007)
T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91, 014101 (2003)
A.E. Motter, C. Zhou, J. Kurths, Phys. Rev. E 71, 016116 (2005)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)
L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 80, 2109 (1998)
C. Zhou, A.E. Motter, J. Kurhts, Phys. Rev. Lett. 96, 034101 (2006)
A.E. Motter, C. Zhou, J. Kurths, Europhys. Lett. 69, 334 (2005)
K.S. Fink, G. Johnson, T.L. Carroll, D. Mar, L.M. Pecora, Phys. Rev. E 61, 5080 (2000)
X. Wang, G. Chen, IEEE Trans. Circuits Syst. I 49, 54 (2002)
I.V. Belykh, V.N. Belykh, M. Hasler, Phys. D 195, 159 (2004)
G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd edn. (Johns Hopkins University Press, Baltimore, MD, 1996)
L. Wang, F. Du, H.P. Dai, Y.X. Sun, Eur. Phy. J. B 53, 361 (2006)
L. Wang, H.P. Dai, Y.X. Sun, Physica A 383, 763 (2007)
L. Wang, H.P. Dai, Y.X. Sun, J. Phys. A: Math. Theor. 40, 13279 (2007)
L.O. Chua, C.W. Wu, A. Huang, G.Q. Zhong, IEEE Trans. Circuits Syst. I 40, 732 (1993)
W. Lin, Y. He. Chaos 15, 023705 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Dai, H., Dong, H. et al. Adaptive synchronization of weighted complex dynamical networks through pinning. Eur. Phys. J. B 61, 335–342 (2008). https://doi.org/10.1140/epjb/e2008-00081-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2008-00081-5