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This paper deals deals with the problem of generalized synchronization (GS) between two different complex networks with time-varying delay coupling. By designing a nonlinear adaptive controller, the GS between these two networks is achieved based on Barbalat's lemma. Furthermore, when the topological structures of two networks are fully unknown, the GS problem is also discussed. Numerical simulations are provided to demonstrate the effectiveness of the proposed methods.
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Keywords:
- complex network /
- generalized synchronization /
- time-varying delay coupling /
- adaptive control
[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Albert R, Jeong H, Barabai A L 1999 Nature 401 130
[3] Newman M E J, Strogatz S H, Watts D J 2001 Phys. Rev. E 64 26118
[4] Ravasz E, Barabai A L 2003 Phys. Rev. E 67 26112
[5] Haken H 2005 Physica D 205 1
[6] Wang X F, Chen G 2002 IEEE Transactions on Circuits and Systems I 49 54
[7] Wu C W 2006 IEEE Trans. Autom. Control 51 1207
[8] Sorrentino F, BernardoMD, Cuellar G H, Boccaletti S 2006 Physica D 224 123
[9] Zhou J, Lu J A, Lv J H 2006 IEEE Trans. Autom. Control 51 652
[10] Zhou J, Lu J A, Lv J H 2008 Automatica 44 996
[11] Luo Q, Wu W, Li L X, Yang Y X and Peng H P 2008 Acta Phys. Sin. 58 1529 (in Chinese) [罗群, 吴薇, 李丽香, 杨义先, 彭海朋 2008 57 1529]
[12] Lv L, Zhang C 2009 Acta Phys. Sin. 59 1462 (in Chinese) [吕翎, 张超 2009 58 1462]
[13] Li C P, Sun W, Kurths J 2007 Phys. Rev. E 76 046204
[14] Tang H W, Cheng L, Lu J A, Tse C K 2008 Physica A 387 5623
[15] Chen J R, Jiao L C, Wu J S, Wang X H 2009 Chin. Phys. Lett. 26 060505
[16] Hu M F, Yang Y Q, Xu Z Y, Zhang R, Guo L X 2007 Physica A 381 457
[17] Sun M, Zeng C Y, Tian L X 2008 Phys. Lett. A 372 6904
[18] Sun M, Zeng C Y, Tian L X 2009 Chin. Phys. Lett. 26 010501
[19] Zheng S, Bi Q S, Cai G L 2009 Phys. Lett. A 373 1553
[20] Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 027201
[21] Sun M, Zeng C Y, Tian L X 2010 Commun. Nonlinear. Sci. Numer. Simul. 15 2162
[22] Wu X Q, Zheng W X, Zhou J 2009 Chaos 19 013109
[23] Zhou J, Lu J A 2007 Physica A 386 481
[24] Wu X Q 2008 Physica A 387 997
[25] Liu H, Lu J A, Lv J H, Hill D J 2009 Automatica 45 1799
[26] Chen L, Lu J A, Tse C K 2009 IEEE Transactions on Circuits and Systems II 56 310
[27] Lee T C, Jiang Z P 2005 IEEE Trans. Autom. Control 50 1147
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Albert R, Jeong H, Barabai A L 1999 Nature 401 130
[3] Newman M E J, Strogatz S H, Watts D J 2001 Phys. Rev. E 64 26118
[4] Ravasz E, Barabai A L 2003 Phys. Rev. E 67 26112
[5] Haken H 2005 Physica D 205 1
[6] Wang X F, Chen G 2002 IEEE Transactions on Circuits and Systems I 49 54
[7] Wu C W 2006 IEEE Trans. Autom. Control 51 1207
[8] Sorrentino F, BernardoMD, Cuellar G H, Boccaletti S 2006 Physica D 224 123
[9] Zhou J, Lu J A, Lv J H 2006 IEEE Trans. Autom. Control 51 652
[10] Zhou J, Lu J A, Lv J H 2008 Automatica 44 996
[11] Luo Q, Wu W, Li L X, Yang Y X and Peng H P 2008 Acta Phys. Sin. 58 1529 (in Chinese) [罗群, 吴薇, 李丽香, 杨义先, 彭海朋 2008 57 1529]
[12] Lv L, Zhang C 2009 Acta Phys. Sin. 59 1462 (in Chinese) [吕翎, 张超 2009 58 1462]
[13] Li C P, Sun W, Kurths J 2007 Phys. Rev. E 76 046204
[14] Tang H W, Cheng L, Lu J A, Tse C K 2008 Physica A 387 5623
[15] Chen J R, Jiao L C, Wu J S, Wang X H 2009 Chin. Phys. Lett. 26 060505
[16] Hu M F, Yang Y Q, Xu Z Y, Zhang R, Guo L X 2007 Physica A 381 457
[17] Sun M, Zeng C Y, Tian L X 2008 Phys. Lett. A 372 6904
[18] Sun M, Zeng C Y, Tian L X 2009 Chin. Phys. Lett. 26 010501
[19] Zheng S, Bi Q S, Cai G L 2009 Phys. Lett. A 373 1553
[20] Shang Y, Chen M Y, Kurths J 2009 Phys. Rev. E 80 027201
[21] Sun M, Zeng C Y, Tian L X 2010 Commun. Nonlinear. Sci. Numer. Simul. 15 2162
[22] Wu X Q, Zheng W X, Zhou J 2009 Chaos 19 013109
[23] Zhou J, Lu J A 2007 Physica A 386 481
[24] Wu X Q 2008 Physica A 387 997
[25] Liu H, Lu J A, Lv J H, Hill D J 2009 Automatica 45 1799
[26] Chen L, Lu J A, Tse C K 2009 IEEE Transactions on Circuits and Systems II 56 310
[27] Lee T C, Jiang Z P 2005 IEEE Trans. Autom. Control 50 1147
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