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Based on Lyapunov stability theory, by introducing a special matrix structure, a modified active control is proposed for the generalized projective synchronization of chaotic system. Compared with the traditional active control, the modified active control is independent of the Routh-Hurwitz criterion, which means the complexity of active control is simplified. The method is successfully applied to the energy resource system and nuclear spin generator system. Compared with other method, the proposed method, which could realize the generalized projective synchronization between both identical systems and different systems, is shown to be simple, direct, stable and efficient. Numerical simulation is provided to show the validity of the theoretical analysis and the effectiveness of the method.
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Keywords:
- modified active control /
- generalized projective synchronization /
- special matrix structure
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Zheng Z G, Hu G, Zhou C S, Hu B B 2000 Acta Phys. Sin. 49 2320 (in Chinese) [郑志刚、胡 岗、周昌松、胡斑比 2000 49 2320]
[3] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[4] Feng Y L, Shen K 2008 Chin. Phys. B 17 550
[5] Suwat K 2009 Phys. Lett. A 373 2837
[6] Liu J, Chen S H, Lu J A 2003 Acta Phys. Sin. 52 1595 (in Chinese) [刘 杰、陈士华、陆君安 2003 52 1595]
[7] Yang W, Sun J T 2010 Phys. Lett. A 374 557
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[9] Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802(in Chinese)[蔡 娜、井元伟、张嗣瀛 2009 58 802]
[10] Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721(in Chinese)[李秀春、徐 伟、肖玉柱 2008 57 4721]
[11] Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529
[12] Ma T D, Zhang H G, Fu J 2008 Chin. Phys. B 17 4407
[13] Li J F, Liu Y P, Gan Y 2009 Acta Phys. Sin. 58 779(in Chinese)[李建芬、李 农、刘宇平、甘 轶 2009 58 779]
[14] Lou X Y, Cui B T 2008 Chin. Phys. B 17 520
[15] Qin J, Yu H J 2007 Acta Phys. Sin. 56 6828(in Chinese) [秦 洁、于洪洁 2007 56 6828]
[16] Li C B, Wang D C 2009 Acta Phys. Sin. 58 764(in Chinese)[李春彪、王德纯 2009 58 764]
[17] Mainieri R, Rehacek J 1999 Phys. Rev. Lett. 82 3042
[18] Xu D, Chee C Y 2002 Phys. Rev. E 66 046218
[19] Yan J, Li C 2005 Chaos, Solitons and Fractals 26 1119
[20] Yau H T 2008 Phys. Lett. A 372 2380
[21] Li G H 2007 Chaos, Solitons and Fractals 32 1454
[22] Hu J B, Han Y, Zhao L D 2010 Commun. Nonlinear. Sci. Numer. Simulat. 15 115
[23] Bai E W,Karl E L 1997 Chaos, Solitons and Fractals 8 51
[24] Sun M, Tian L X, Fu Y 2007 Chaos, Solitons and Fractals 32 168
[25] Ayman A S 2009 Chaos, Solitons and Fractals 42 1926
[26] Li R H, Xu W, Li S 2007 Phys. Lett. A 367 199
[27] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p26 (in Chinese)[刘秉正、彭建华 2004 非线性动力学(北京:高等教育出版社) 第26页]
[28] Sun M, Tian L X, Fu Y 2007 Chaos, Solitons and Fractals 31 879
[29] Sun M, Tian L X, Xu J 2007 Chaos, Solitons and Fractals 32 1725
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Zheng Z G, Hu G, Zhou C S, Hu B B 2000 Acta Phys. Sin. 49 2320 (in Chinese) [郑志刚、胡 岗、周昌松、胡斑比 2000 49 2320]
[3] Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[4] Feng Y L, Shen K 2008 Chin. Phys. B 17 550
[5] Suwat K 2009 Phys. Lett. A 373 2837
[6] Liu J, Chen S H, Lu J A 2003 Acta Phys. Sin. 52 1595 (in Chinese) [刘 杰、陈士华、陆君安 2003 52 1595]
[7] Yang W, Sun J T 2010 Phys. Lett. A 374 557
[8] Liu Y Z, Jiang C S, Lin C S 2007 Acta Phys. Sin. 56 0707 (in Chinese) [刘扬正、姜长圣、林长圣 2007 56 0707]
[9] Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802(in Chinese)[蔡 娜、井元伟、张嗣瀛 2009 58 802]
[10] Li X C, Xu W, Xiao Y Z 2008 Acta Phys. Sin. 57 4721(in Chinese)[李秀春、徐 伟、肖玉柱 2008 57 4721]
[11] Zhao Y, Zhang H G, Zheng C D 2008 Chin. Phys. B 17 529
[12] Ma T D, Zhang H G, Fu J 2008 Chin. Phys. B 17 4407
[13] Li J F, Liu Y P, Gan Y 2009 Acta Phys. Sin. 58 779(in Chinese)[李建芬、李 农、刘宇平、甘 轶 2009 58 779]
[14] Lou X Y, Cui B T 2008 Chin. Phys. B 17 520
[15] Qin J, Yu H J 2007 Acta Phys. Sin. 56 6828(in Chinese) [秦 洁、于洪洁 2007 56 6828]
[16] Li C B, Wang D C 2009 Acta Phys. Sin. 58 764(in Chinese)[李春彪、王德纯 2009 58 764]
[17] Mainieri R, Rehacek J 1999 Phys. Rev. Lett. 82 3042
[18] Xu D, Chee C Y 2002 Phys. Rev. E 66 046218
[19] Yan J, Li C 2005 Chaos, Solitons and Fractals 26 1119
[20] Yau H T 2008 Phys. Lett. A 372 2380
[21] Li G H 2007 Chaos, Solitons and Fractals 32 1454
[22] Hu J B, Han Y, Zhao L D 2010 Commun. Nonlinear. Sci. Numer. Simulat. 15 115
[23] Bai E W,Karl E L 1997 Chaos, Solitons and Fractals 8 51
[24] Sun M, Tian L X, Fu Y 2007 Chaos, Solitons and Fractals 32 168
[25] Ayman A S 2009 Chaos, Solitons and Fractals 42 1926
[26] Li R H, Xu W, Li S 2007 Phys. Lett. A 367 199
[27] Liu B Z, Peng J H 2004 Nonlinear Dynamics (Beijing: Higher Education Press) p26 (in Chinese)[刘秉正、彭建华 2004 非线性动力学(北京:高等教育出版社) 第26页]
[28] Sun M, Tian L X, Fu Y 2007 Chaos, Solitons and Fractals 31 879
[29] Sun M, Tian L X, Xu J 2007 Chaos, Solitons and Fractals 32 1725
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