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In this paper we study the chaos synchronization of a new Lü chaotic system containing constants via three methods, i.e., state observer, active control method, and backstepping method. Based on the above three methods, the we design an adaptive controller according to the Lyapunov stability theory which proves that the controller can well realize the asymptotical synchronization between two identical systems. Through numerical simulation, we further verify the effectiveness and the advantage of the above three synchronization methods. The synchronization method based on state observer is believed to be more flexible and efficient through the comparative analysis of three kinds of synchronization methods.
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Keywords:
- chaos synchronization /
- observer synchronization /
- active control /
- backstepping
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Carroll T L, Pecora L M 1991 IEEE T. Circuit-I 38 453
[3] Chua L O, Kocarev L, Eckert K 1992 Int. J. Bifurcat. Chaos 2 705
[4] Kocarev L 1993 Int. J. Bifurcat. Chaos 3 479
[5] John J K, Amritkar R E 1994 Int. J. Bifurcat. Chaos 4 1687
[6] Lü J H, Chen G R 2002 Int. J. Bifurcat. Chaos 12 659
[7] Guan X P, Fan Z P, Chen C L 2002 Chaotic Control And Its Application In Secret Communication (Beijing: Defense Industry Press) p183(in Chinese)[关新平、范正平、陈彩莲等 2002混沌控制及其在保密通信中的应用(北京:国防工业出版社) 第183页]
[8] Chen G R, Lv J H 2002 Dynamics Analysis, Control And Synchronization On Lorenz System Race(Beijing:Science Press) p55(in Chinese)[陈关荣、吕金虎 2002 Lorenz系统族的动力学分析,控制与同步(北京:科学出版社) 第55页]
[9] Wang X Y, Wu X J 2006 Chaos 16 033121
[10] Wang Z S, Zhang H G, Wang Z L 2006 Acta Phys. Sin. 55 2687(in Chinese)[王占山、张化光、王智良 2006 物理学报55 2687] 〖11] Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147(in Chinese) [张化光、马大中、王占山、冯 健 2010 物理学报 59 147]
[11] Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE T. Syst. Man. Cy. B 40 831
[12] Wang T S, Wang X Y 2011 Commun. Nonlinear Sci. Numer. Simul. 16 1464
[13] Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE T. Neural Networ. 18 1841
[14] Yang D S,Zhang H G, Zhao Y, Song C H,Wang Y C 2010 Acta Phys. Sin. 59 1562(in Chinese)[杨东升、张化光、赵 琰、宋崇辉、王迎春 2010 物理学报 59 1562]
[15] Zhang H G, Liu D R, Wang Z L 2009 Control- ling Chaos: Suppression, Synchronization and Chaotification (London: Springer) p246
[16] Lü J H, Chen G R, Cheng D Z 2004 Int. J. Bifurcat. Chaos 14 1507
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Carroll T L, Pecora L M 1991 IEEE T. Circuit-I 38 453
[3] Chua L O, Kocarev L, Eckert K 1992 Int. J. Bifurcat. Chaos 2 705
[4] Kocarev L 1993 Int. J. Bifurcat. Chaos 3 479
[5] John J K, Amritkar R E 1994 Int. J. Bifurcat. Chaos 4 1687
[6] Lü J H, Chen G R 2002 Int. J. Bifurcat. Chaos 12 659
[7] Guan X P, Fan Z P, Chen C L 2002 Chaotic Control And Its Application In Secret Communication (Beijing: Defense Industry Press) p183(in Chinese)[关新平、范正平、陈彩莲等 2002混沌控制及其在保密通信中的应用(北京:国防工业出版社) 第183页]
[8] Chen G R, Lv J H 2002 Dynamics Analysis, Control And Synchronization On Lorenz System Race(Beijing:Science Press) p55(in Chinese)[陈关荣、吕金虎 2002 Lorenz系统族的动力学分析,控制与同步(北京:科学出版社) 第55页]
[9] Wang X Y, Wu X J 2006 Chaos 16 033121
[10] Wang Z S, Zhang H G, Wang Z L 2006 Acta Phys. Sin. 55 2687(in Chinese)[王占山、张化光、王智良 2006 物理学报55 2687] 〖11] Zhang H G, Ma D Z, Wang Z S, Feng J 2010 Acta Phys. Sin. 59 147(in Chinese) [张化光、马大中、王占山、冯 健 2010 物理学报 59 147]
[11] Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE T. Syst. Man. Cy. B 40 831
[12] Wang T S, Wang X Y 2011 Commun. Nonlinear Sci. Numer. Simul. 16 1464
[13] Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE T. Neural Networ. 18 1841
[14] Yang D S,Zhang H G, Zhao Y, Song C H,Wang Y C 2010 Acta Phys. Sin. 59 1562(in Chinese)[杨东升、张化光、赵 琰、宋崇辉、王迎春 2010 物理学报 59 1562]
[15] Zhang H G, Liu D R, Wang Z L 2009 Control- ling Chaos: Suppression, Synchronization and Chaotification (London: Springer) p246
[16] Lü J H, Chen G R, Cheng D Z 2004 Int. J. Bifurcat. Chaos 14 1507
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