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In this paper, We investigate the adaptive anti-synchronization in a unified hyperchaotic system with unknown parameters. First, according to the Lyapunov stability theory, We achieve an adaptive controller and show that the controller can make a unified hyperchaotic system with unknown parameters asymptotically stable at a fixed point. Second, by the adaptive anti-synchronization method, We design an adaptive anti-synchronous controller and thereby achieve the hyperchaotic system synchronization. Finally, numerical simulations show the effectiveness of the scheme.
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Wang X Y 2003 Chaos in the Complex Nonlinearity System (Beijing: Electronics Industry Press) Chapt. 2 (in Chinese) [王兴元2003 复杂非线性系统中的混沌(北京:电子工业出版社)第二章]
[3] Chen G R, Lü J H 2003 Dynamics of the Lorenz systems family: Analysis, control and synchronization (Beijing: Science Press) Chapt. 8 (in Chinese)[陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步(北京:科学出版社)第八章]
[4] Zhang H G, Wang Z L, Huang W 2003 Control Theory of Chaotic Systems (Shenyang: Northeastern University Press) Chapt. 4 (in Chinese) [张化光、王智良、黄 玮 2003 混沌系统的控制理论 (沈阳:东北大学出版社) 第四章]
[5] Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos: Suppression, Synchronization, and Chaotification (New York: Springer)
[6] Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[7] Wu Y X, Huang X, Gao J, Zheng Z G 2007 Acta Phys. Sin. 56 3803(in Chinese) [吴玉喜、黄 霞、高 建、郑志刚 2007 物理学报 56 3803]
[8] Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comp. 217 2481
[9] Zhang H G, Xie Y, Wang Z, Zheng C 2007 IEEE Trans. Neural Networks 18 1841
[10] Meng J, Wang X Y 2008 Chin. J. Comp. Phys. 25 243 (in Chinese) [孟 娟、王兴元 2008 计算物理 25 243]
[11] Wang X Y, Wang Y 2007 Inter. J. Mod. Phys. B 21 3017
[12] Li N, Li J F,Liu Y P 2010 Acta Phys. Sin. 59 5954(in Chinese) [李 农、李建芬、刘宇平 2010 物理学报 59 5954]
[13] Wu X J, Wang X Y 2009 J. Syst. Engin. 24 136 (in Chinese) [武相军、王兴元 2009 系统工程学报 24 136]
[14] Xiao J 2010 Chin. Phys. B 19 100505
[15] Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[16] Lü J H, Chen G R 2002 Inter. J. Bifurca. and Chaos 12 659
[17] Wang X Y, Zhao G B 2010 Inter. J. Mod. Phys. B 24 4619
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Wang X Y 2003 Chaos in the Complex Nonlinearity System (Beijing: Electronics Industry Press) Chapt. 2 (in Chinese) [王兴元2003 复杂非线性系统中的混沌(北京:电子工业出版社)第二章]
[3] Chen G R, Lü J H 2003 Dynamics of the Lorenz systems family: Analysis, control and synchronization (Beijing: Science Press) Chapt. 8 (in Chinese)[陈关荣、吕金虎 2003 Lorenz系统族的动力学分析、控制与同步(北京:科学出版社)第八章]
[4] Zhang H G, Wang Z L, Huang W 2003 Control Theory of Chaotic Systems (Shenyang: Northeastern University Press) Chapt. 4 (in Chinese) [张化光、王智良、黄 玮 2003 混沌系统的控制理论 (沈阳:东北大学出版社) 第四章]
[5] Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos: Suppression, Synchronization, and Chaotification (New York: Springer)
[6] Zhang H G, Ma T D, Yu W, Fu J 2008 Chin. Phys. B 17 3616
[7] Wu Y X, Huang X, Gao J, Zheng Z G 2007 Acta Phys. Sin. 56 3803(in Chinese) [吴玉喜、黄 霞、高 建、郑志刚 2007 物理学报 56 3803]
[8] Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comp. 217 2481
[9] Zhang H G, Xie Y, Wang Z, Zheng C 2007 IEEE Trans. Neural Networks 18 1841
[10] Meng J, Wang X Y 2008 Chin. J. Comp. Phys. 25 243 (in Chinese) [孟 娟、王兴元 2008 计算物理 25 243]
[11] Wang X Y, Wang Y 2007 Inter. J. Mod. Phys. B 21 3017
[12] Li N, Li J F,Liu Y P 2010 Acta Phys. Sin. 59 5954(in Chinese) [李 农、李建芬、刘宇平 2010 物理学报 59 5954]
[13] Wu X J, Wang X Y 2009 J. Syst. Engin. 24 136 (in Chinese) [武相军、王兴元 2009 系统工程学报 24 136]
[14] Xiao J 2010 Chin. Phys. B 19 100505
[15] Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[16] Lü J H, Chen G R 2002 Inter. J. Bifurca. and Chaos 12 659
[17] Wang X Y, Zhao G B 2010 Inter. J. Mod. Phys. B 24 4619
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