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In this paper, we introduce a type of chaotic synchronization, where two chaotic systems are synchronized based on a function matrix. In particular, each drive system state synchronizes with a certain combination of response system states. Based on linear system theory and the pole placement technique, the scheme is given and illustrated with hyperchaotic Lorenz system and Lorenz chaotic system. Numerical simulations are carried out to verify the effectiveness of the proposed scheme.
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Keywords:
- function matrix /
- chaos synchronization /
- lag synchronization
[1] Pecora L M, Canoll T L 1990 Phys. Rev. Lett. 64 821
[2] Han D, Zhu F L 2013 Acta Phys. Sin. 62 120513 (in Chinese) [韩冬, 朱芳来 2013 62 120513]
[3] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 59 2305]
[4] Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) [王兴元, 武相军 2006 55 605]
[5] Mainieri R, Rehaced J 1999 Phys. Rev. Lett. 82 3042
[6] Li Z, Han C Z 2002 Chin. Phys. 11 666
[7] Li Z, Han C Z 2002 Chin. Phys. 11 9
[8] Gao X, Yu J B 2005 Chaos Soliton. Fract. 26 141
[9] Rosenblum M G, Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 4193
[10] Akcakaya M, Nehorai A 2010 IEEE Trans. Signal Process 58 4994
[11] Du H Y 2012 Function Projective Synchronization of Chaotic Theory and Its Application in Secure Communication (Heilongjiang: Heilongjiang University Press) p10 (in Chinese) [杜洪越 2012 混沌函数投影同步理论及其保密通信应用 (黑龙江: 黑龙江大学出版社) 第10页]
[12] Xu D, Li Z 2002 Int. J. Bifurcat. Chaos 12 1395
[13] Hu M F, Xu Z Y, Rong Z 2008 Commun. Nonlinear Sci. 13 456
[14] Li G H 2007 Chaos Soliton. Fract. 32 1786
[15] Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505
[16] Grassi G, Miller D A 2012 Appl. Math. Comput. 218 6118
[17] Meng J, Wang X Y 2007 Acta Phys. Sin. 56 5142 (in Chinese) [孟娟, 王兴元 2007 56 5142]
[18] Lorenz E N 1963 J. Atmos. Sci. 20 130
[19] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元, 王明军 2007 56 5136]
[20] Ogorzalek M 1993 IEEE Trans. Circuits I 40 693
[21] Tigan G H 2005 Scientific Bulletin of the Politehnica University of Timisoara 50 61
[22] Wang Z, Sun W 2013 Acta Phys. Sin. 62 020511 (in Chinese) [王震, 孙卫 2013 62 020511]
[23] Matsumoto T, Chua L O, Kobayashi K 1986 IEEE Trans. Circuits I 33 1143
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[1] Pecora L M, Canoll T L 1990 Phys. Rev. Lett. 64 821
[2] Han D, Zhu F L 2013 Acta Phys. Sin. 62 120513 (in Chinese) [韩冬, 朱芳来 2013 62 120513]
[3] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 59 2305]
[4] Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 605 (in Chinese) [王兴元, 武相军 2006 55 605]
[5] Mainieri R, Rehaced J 1999 Phys. Rev. Lett. 82 3042
[6] Li Z, Han C Z 2002 Chin. Phys. 11 666
[7] Li Z, Han C Z 2002 Chin. Phys. 11 9
[8] Gao X, Yu J B 2005 Chaos Soliton. Fract. 26 141
[9] Rosenblum M G, Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 4193
[10] Akcakaya M, Nehorai A 2010 IEEE Trans. Signal Process 58 4994
[11] Du H Y 2012 Function Projective Synchronization of Chaotic Theory and Its Application in Secure Communication (Heilongjiang: Heilongjiang University Press) p10 (in Chinese) [杜洪越 2012 混沌函数投影同步理论及其保密通信应用 (黑龙江: 黑龙江大学出版社) 第10页]
[12] Xu D, Li Z 2002 Int. J. Bifurcat. Chaos 12 1395
[13] Hu M F, Xu Z Y, Rong Z 2008 Commun. Nonlinear Sci. 13 456
[14] Li G H 2007 Chaos Soliton. Fract. 32 1786
[15] Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505
[16] Grassi G, Miller D A 2012 Appl. Math. Comput. 218 6118
[17] Meng J, Wang X Y 2007 Acta Phys. Sin. 56 5142 (in Chinese) [孟娟, 王兴元 2007 56 5142]
[18] Lorenz E N 1963 J. Atmos. Sci. 20 130
[19] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 5136 (in Chinese) [王兴元, 王明军 2007 56 5136]
[20] Ogorzalek M 1993 IEEE Trans. Circuits I 40 693
[21] Tigan G H 2005 Scientific Bulletin of the Politehnica University of Timisoara 50 61
[22] Wang Z, Sun W 2013 Acta Phys. Sin. 62 020511 (in Chinese) [王震, 孙卫 2013 62 020511]
[23] Matsumoto T, Chua L O, Kobayashi K 1986 IEEE Trans. Circuits I 33 1143
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