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The synchronization in complex network model with time-delay nodes is investigated. The model is applicable for two sorts of complex networks. With linear feedback controller and adaptive feedback controller, positive definite functions are designed respectively. The sufficient conditions of synchronization are given by Lyapunov stability theory. Finally, numerical simulations show the effectiveness of the synchronization in complex networks.
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Keywords:
- complex network /
- delay /
- synchronization
[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabási A L, Albert R 1999 Science 286 509
[3] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[4] Newman M E J 2003 SIAM Rev. 45 67
[5] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[6] Wang X F, Li X, Chen G R 2006 Theory and Application of Complex Networks (Beijing: Tsinghua University Press) p49 (in Chinese) [汪小帆, 李翔, 陈关荣 2006 复杂网络理论及其应用 (北京: 清华大学出版社) 第49页]
[7] Hong H, Kim B J, Choi M Y, Park H 2004 Phys. Rev. E 69 067105
[8] Comellas F, Gago S 2007 J. Phys. A 40 4483
[9] Jalili M 2011 Physica A 390 4588
[10] Wang Y W, Wang H O, Xiao J W, Guan Z H 2010 Automatica 46 197
[11] Reddy D V R, Sen A, Johnson G L 2000 Phys. Rev. Lett. 85 3381
[12] Kozyreff G, Vladimirov A, Mandel P 2000 Phys. Rev. Lett. 85 3809
[13] Lindsey W C, Chen J H 1996 Eur. T. Telecommun. 7 25
[14] Li C G, Chen G R 2004 Physica A 343 263
[15] Wang Y W, Yang M, Wang H O 2009 IEEE Trans. Circuits Syst. I 56 2100
[16] Liu Y, Wang Z 2008 IEEE T. Man Cy. B 38 1314
[17] Guo L L, Wang Y W, Wang H O, Huang Y H 2009 IEEE International Symposium on Intelligent Control Part of IEEE Multi-Conference on Systems and Control Saint Petersburg, Russia, July 8-10, 2009 p177
[18] Gao H J, Lam J, Chen G R 2006 Phys. Lett. A 360 263
[19] Zhang H G, Gong D W, Wang Z S 2011 Chin. Phys. B 20 040512
[20] Wu J S, Jiao L C 2007 Physica A 386 513
[21] Li K, Guan S G, Gong X F, Lai C H 2008 Phys. Lett. A 372 7133
[22] Li H J, Yue D 2009 J. Comput. Appl. Math. 232 149
[23] Wang J A 2012 Acta Phys. Sin. 61 020509 (in Chinese) [王健安 2012 61 020509
[24] Yue D, Li H J 2010 Neurocomputing 73 809
[25] Guo W L, Austin F, Chen S H, Sun W 2009 Phys. Lett. A 373 1565
[26] Gao Y, Li L X, Peng H P, Yang Y X, Zhang X H 2008 Acta Phys. Sin. 57 1444 (in Chinese) [高洋, 李丽香, 彭海朋, 杨义先, 张小红 2008 57 1444]
[27] Bian Q X, Yao H X 2010 Acta Phys. Sin. 59 3027 (in Chinese) [卞秋香, 姚洪兴 2010 59 3027]
[28] Luo Q, Wu W, Li L X, Yang Y X, Peng H P 2008 Acta Phys. Sin. 57 1529 (in Chinese) [罗群, 吴薇, 李丽香, 杨义先, 彭海朋 2008 57 1529]
[29] Guan X P, Chen C L, Peng H P, Fan Z P 2003 Int. J. Bifur. Chaos 13 193
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabási A L, Albert R 1999 Science 286 509
[3] Albert R, Barabási A L 2002 Rev. Mod. Phys. 74 47
[4] Newman M E J 2003 SIAM Rev. 45 67
[5] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[6] Wang X F, Li X, Chen G R 2006 Theory and Application of Complex Networks (Beijing: Tsinghua University Press) p49 (in Chinese) [汪小帆, 李翔, 陈关荣 2006 复杂网络理论及其应用 (北京: 清华大学出版社) 第49页]
[7] Hong H, Kim B J, Choi M Y, Park H 2004 Phys. Rev. E 69 067105
[8] Comellas F, Gago S 2007 J. Phys. A 40 4483
[9] Jalili M 2011 Physica A 390 4588
[10] Wang Y W, Wang H O, Xiao J W, Guan Z H 2010 Automatica 46 197
[11] Reddy D V R, Sen A, Johnson G L 2000 Phys. Rev. Lett. 85 3381
[12] Kozyreff G, Vladimirov A, Mandel P 2000 Phys. Rev. Lett. 85 3809
[13] Lindsey W C, Chen J H 1996 Eur. T. Telecommun. 7 25
[14] Li C G, Chen G R 2004 Physica A 343 263
[15] Wang Y W, Yang M, Wang H O 2009 IEEE Trans. Circuits Syst. I 56 2100
[16] Liu Y, Wang Z 2008 IEEE T. Man Cy. B 38 1314
[17] Guo L L, Wang Y W, Wang H O, Huang Y H 2009 IEEE International Symposium on Intelligent Control Part of IEEE Multi-Conference on Systems and Control Saint Petersburg, Russia, July 8-10, 2009 p177
[18] Gao H J, Lam J, Chen G R 2006 Phys. Lett. A 360 263
[19] Zhang H G, Gong D W, Wang Z S 2011 Chin. Phys. B 20 040512
[20] Wu J S, Jiao L C 2007 Physica A 386 513
[21] Li K, Guan S G, Gong X F, Lai C H 2008 Phys. Lett. A 372 7133
[22] Li H J, Yue D 2009 J. Comput. Appl. Math. 232 149
[23] Wang J A 2012 Acta Phys. Sin. 61 020509 (in Chinese) [王健安 2012 61 020509
[24] Yue D, Li H J 2010 Neurocomputing 73 809
[25] Guo W L, Austin F, Chen S H, Sun W 2009 Phys. Lett. A 373 1565
[26] Gao Y, Li L X, Peng H P, Yang Y X, Zhang X H 2008 Acta Phys. Sin. 57 1444 (in Chinese) [高洋, 李丽香, 彭海朋, 杨义先, 张小红 2008 57 1444]
[27] Bian Q X, Yao H X 2010 Acta Phys. Sin. 59 3027 (in Chinese) [卞秋香, 姚洪兴 2010 59 3027]
[28] Luo Q, Wu W, Li L X, Yang Y X, Peng H P 2008 Acta Phys. Sin. 57 1529 (in Chinese) [罗群, 吴薇, 李丽香, 杨义先, 彭海朋 2008 57 1529]
[29] Guan X P, Chen C L, Peng H P, Fan Z P 2003 Int. J. Bifur. Chaos 13 193
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