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A unified method for the projective synchronization of chaotic system is proposed in this paper. The universal model of chaotic projective synchronization is established by constructing a generalized proportion matrix and an appropriate response system. All kinds of synchronized schemes can be achieved by varying the generalized proportion matrix, including generalized projective synchronization, dislocated projective synchronization and generalized hybrid dislocated projective synchronization and so on. The stability analysis in the paper is proved using Lyapunov stability theory. Numerical simulations of generalized hybrid dislocated projective synchronization for multiscroll chaotic attractors system and hyperchaotic Qi system verify the effectiveness of the proposed method.
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Rosenblum M G, Pikovsky A S, Kurths J 1996 Phys. Rev. Lett. 76 1804
[3] Kocarev L, Parlitz U 1996 Phys. Rev. Lett. 76 1816
[4] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese)[王兴元、孟 娟 2008 物理学报 57 726]
[5] 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 物理学报 52 1595]
[6] Wang X Y, Wang Y 2007 Acta Phys. Sin. 56 2498 (in Chinese) [王兴元、王 勇 2007 物理学报 56 2498]
[7] Du H, Zeng Q, Wong C 2008 Phys. Lett. A 372 5402
[8] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 1847
[9] Li G H 2007 Chaos, Soliton. Fract. 32 1454
[10] Du H, Zeng Q, Wong C 2009 Chaos, Soliton. Fract. 42 2399
[11] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 3743
[12] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2265 (in Chinese) [王健安、刘 贺 2010 物理学报 59 2265]
[13] Hu M F, Xu Z Y 2007 Syst. Eng. Electr. 29 1346 (in Chinese)[胡满峰、徐振源 2007 系统工程与电子技术 29 1346]
[14] Min F H, Wang E R 2010 Acta Phys. Sin. 59 7657 (in Chinese)[闵富红、王恩荣 2010 物理学报 59 7657]
[15] Xu Y H, Zhou W N, Fang J A 2009 Chaos, Soliton. Fract. 42 1305
[16] Lü J H, Chen G R, Yu X G, Leung H 2004 IEEE Trans. Circ. Syst. I 51 2476
[17] Qi G Y, Michael A, Barend J, Chen G R 2009 Chaos, Soliton. Fract. 40 2544
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Rosenblum M G, Pikovsky A S, Kurths J 1996 Phys. Rev. Lett. 76 1804
[3] Kocarev L, Parlitz U 1996 Phys. Rev. Lett. 76 1816
[4] Wang X Y, Meng J 2008 Acta Phys. Sin. 57 726 (in Chinese)[王兴元、孟 娟 2008 物理学报 57 726]
[5] 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 物理学报 52 1595]
[6] Wang X Y, Wang Y 2007 Acta Phys. Sin. 56 2498 (in Chinese) [王兴元、王 勇 2007 物理学报 56 2498]
[7] Du H, Zeng Q, Wong C 2008 Phys. Lett. A 372 5402
[8] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 1847
[9] Li G H 2007 Chaos, Soliton. Fract. 32 1454
[10] Du H, Zeng Q, Wong C 2009 Chaos, Soliton. Fract. 42 2399
[11] Sudheer K S, Sabir M 2009 Phys. Lett. A 373 3743
[12] Wang J A, Liu H P 2010 Acta Phys. Sin. 59 2265 (in Chinese) [王健安、刘 贺 2010 物理学报 59 2265]
[13] Hu M F, Xu Z Y 2007 Syst. Eng. Electr. 29 1346 (in Chinese)[胡满峰、徐振源 2007 系统工程与电子技术 29 1346]
[14] Min F H, Wang E R 2010 Acta Phys. Sin. 59 7657 (in Chinese)[闵富红、王恩荣 2010 物理学报 59 7657]
[15] Xu Y H, Zhou W N, Fang J A 2009 Chaos, Soliton. Fract. 42 1305
[16] Lü J H, Chen G R, Yu X G, Leung H 2004 IEEE Trans. Circ. Syst. I 51 2476
[17] Qi G Y, Michael A, Barend J, Chen G R 2009 Chaos, Soliton. Fract. 40 2544
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