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Pinning synchronization of the complex networks with non-delayed and delayed coupling. (English) Zbl 1228.05266
Summary: Without assuming the symmetry of the coupling matrix, we investigate the global synchronization of the complex networks with non-delayed and delayed coupling based on the pinning controllers. Some sufficient conditions for the global synchronization by adding linear and adaptive feedback controllers to a part of nodes are obtained. Numerical examples are also provided to demonstrate the effectiveness of the theory.

MSC:
05C82 Small world graphs, complex networks (graph-theoretic aspects)
34D06 Synchronization of solutions to ordinary differential equations
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[1] Watts, D.J.; Strogatz, S.H., Nature, 393, 440, (1998)
[2] Strogatz, S.H., Nature, 410, 268, (2001)
[3] Barabási, A.L.; Albert, R.; Jeong, H., Physica A, 272, 173, (1999)
[4] Wang, X.F.; Chen, G., IEEE trans. circuits syst. I, 49, 54, (2002)
[5] ()
[6] Chua, L.O., IEEE trans. circuits syst., 42, 557, (1995)
[7] Erdös, P.; Rényi, A., Publ. math., 6, 290, (1959)
[8] Erdös, P.; Rènyi, A., Publ. math. inst. hung. acad. sci., 5, 17, (1960)
[9] Newman, M.E.J., J. stat. phys., 101, 819, (2000)
[10] Barabási, A.L.; Albert, R., Science, 286, 509, (1999)
[11] Lu, W.; Chen, T., Physica D, 213, 214, (2006)
[12] Wu, C.W.; Chua, L.O., IEEE trans. circuits syst. I, 42, 430, (1995)
[13] Cao, J.D.; Lu, J.Q., Chaos, 16, 013133, (2006)
[14] Wu, C.W., Synchronization in complex networks of nonlinear dynamical systems, (2002), World Scientific Singapore
[15] Gu, Y.Q.; Shao, C.; Pu, X.C., Chaos solitons fractals, 28, 480, (2006)
[16] Wang, X.F.; Chen, G.R., Int. J. bifur. chaos, 12, 1, 187, (2002)
[17] Lu, J.H.; Chen, G.R., IEEE trans. automat. control, 50, 6, 841, (2005)
[18] Li, C.G.; Chen, G.R., Physica A, 343, 263, (2004)
[19] Wang, X.F.; Chen, G.R., Physica A, 310, 521, (2002)
[20] Li, X.; Wang, X.F.; Chen, G.R., IEEE trans. circuits syst. I, 51, 2074, (2004)
[21] Chen, T.; Liu, X., IEEE trans. circuits syst. I, 54, 1317, (2007)
[22] Yu, W.W.; Chen, G.R; Lue, J.H., Automatic, 45, 2, 429, (2009)
[23] Zhou, J.; Chen, T., IEEE trans. circuits syst. I, 53, 2, 733, (2006)
[24] Cao, J.; Chen, G.; Li, P., IEEE trans. syst. man cybernet. B: cybernetics, 38, 2, 488, (2008)
[25] Lu, J.; Cao, J., Nonlinear dyn., 53, 1-2, 107, (2008)
[26] Cao, J.; Wang, Z.; Sun, Y., Physica A, 385, 2, 718, (2007)
[27] Sun, W.; Chen, S.; Guo, W.L., Phys. lett. A, 372, 6340, (2008) · Zbl 1225.05223
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