Abstract
This paper presents an adaptive lag synchronization based method for simultaneous identification of topology and parameters of uncertain general complex dynamical networks with and without time delays. Based on Lyapunov stability theorem and LaSalle’s invariance principle, an adaptive controller is designed to realize lag synchronization between drive and response systems, meanwhile, identification criteria of network topology and system parameters are obtained. Numerical simulations illustrate the effectiveness of the proposed method.
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References
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006)
S.H. Strogatz, Nature 410, 268 (2001)
R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
G.V. Osipov, J. Kurths, C. Zhou, Synchronization in Oscillatory Networks (Springer, Berlin, 2007)
M.I. Rabinovich, P. Varona, A.I. Selverston, H.D. Abarbanel, Rev. Mod. Phys. 78, 1213 (2006)
A. Roxin, H. Riecke, S.A. Solla, Phys. Rev. Lett. 92, 198101-1 (2004)
X. Wang, Y. Lu, M. Jiang, Q. Ouyang, Phys. Rev. E 69, 056223-1 (2004)
K. Pyragas, Phys. Rev. E 58, 3067 (1998)
Q. Zhang, J. Lu, J. Lü, C.K. Tse, IEEE Trans. Circuits Syst. II 55, 183 (2008)
D. Yu, M. Righero, L. Kocarev, Phys. Rev. Lett. 97, 188701-1 (2006)
D. Yu, U. Parlitz, Europhys. Lett. 81, 48007 (2008)
D. Yu, Automatica 46, 2035 (2010)
D. Yu, U. Parlitz, Plos One 6, e24333 (2011)
D. Huang, Phys. Rev. E 73, 066204-1 (2006)
H. Liu, J.A. Lu, J. Lü, D.J. Hill, Automatica 45, 1799 (2009)
X. Wu, Physica A 387, 997 (2008)
M. Timme, Phys. Rev. Lett. 98, 224101-1 (2007)
M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 4193 (1997)
N.J. Corron, J.N. Blakely, S.D. Pethel, Chaos 15, 023110-1 (2005)
T. Heil, I. Fischer, W. Elsässer, J. Mulet, C.R. Mirasso, Phys. Rev. Lett. 86, 795 (2001)
M. Ciszak, F. Marino, R. Toral, S. Balle, Phys. Rev. Lett. 93, 114102-1 (2004)
D. Ghosha, A.R. Chowdhury, Nonlinear Anal. Real World Appl. 11, 3059 (2010)
W. Guo, Nonlinear Anal. Real World Appl. 12, 2579 (2011)
Y. Xu, W. Zhou, J. Fang, W. Sun, Phys. Lett. A 374, 3441 (2010)
Q. Wang, Q. Lu, Z. Duan, Int. J. Non-Linear Mech. 45, 640 (2010)
X. Yang, J. Cao, Y. Long, W. Rui, IEEE Trans. Neural. Netw. 21, 1656 (2010)
X. Yang, Q. Zhu, C. Huang, Nonlinear Anal. Real World Appl. 12, 93 (2011)
X.J. Wu, H.T. Lu, Chaos Solitons Fractals 44, 802 (2011)
H.K. Khalil, Nonlinear Systems, 3rd edn. (New Jersey, Prentice Hall, 2002)
J.L. Hindmarsh, R.M. Rose, Proc. Roy. Soc. Lond. B Biol. 221, 81 (1984)
S. Gilbert, Introduction to Linear Algebra, 4th edn., (Wellesley-Cambridge Press, Wellesley MA, 2009)
Y.Q. Che, J. Wang, K.M. Tsang, W.L. Chan, Nonlinear Anal. Real World Appl. 11, 1096 (2010)
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Che, Y., Li, R.X., Han, C.X. et al. Adaptive lag synchronization based topology identification scheme of uncertain general complex dynamical networks. Eur. Phys. J. B 85, 265 (2012). https://doi.org/10.1140/epjb/e2012-20959-7
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DOI: https://doi.org/10.1140/epjb/e2012-20959-7