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The projective synchronization in the unified hyperchaotic system using two control method is studied in this paper. Based on the Lyapunov stability theory, the full state hybrid projective synchronization is achieved via an adaptive controller. It is proved theoretically that the controller can make the states of the dynamical system and the response system with known parameters achieve the asymptotically full state hybrid projective synchronization. An active controller is designed to achieve the projective synchronization. Finally, Numerical simulations show the effectiveness of the two schemes.
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Keywords:
- unified hyperchaotic system /
- adaptive control /
- full state hybrid projective synchronization /
- active control
[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] Li Z, Han C Z 2002 Chin. Phys. 11 666
[5] Yu S M, Ma Z G, Qiu S S, Peng S G, Lin Q H 2004 Chin. Phys. 13 317
[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] Meng J, Wang X Y 2007 Acta Phys. Sin. 56 5142 (in Chinese) [孟 娟、王兴元 2007物理学报 56 5142]
[9] Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾、徐 伟 2007 物理学报 56 3101]
[10] Wang X Y, Wu X J 2007 Acta Phys. Sin. 56 1988 (in Chinese) [王兴元、武相军 2007 物理学报 56 1988]
[11] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元、王明军 2007 物理学报 56 6843]
[12] Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 物理学报 57 4729]
[13] Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006 物理学报 55 6261]
[14] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、黄娟娟 2006 物理学报 55 3997]
[15] Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[16] Mainieri R, Rehacek J 1999 Phys. Rev. Lett.82 3042
[17] Li Z G, Xu D 2004 Chaos, Solitons and Fractals. 22 477
[18] Chee C Y, Xu D 2005 Chaos, Solitons and Fractals. 23 1063
[19] Wen G, Xu D 2005 Chaos, Solitons and Fractals. 26 71
[20] Hu M F, Xu Z Y, Zhang R 2008 Communications in Nonlinear Science and Numerical Simulation 13 456
[21] Lü J H, Chen G R 2002 International Journal of Bifurcation and Chaos. 12 659
[22] Wang X Y, Zhao G B 2010 International Journal of Modern Physics 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] Li Z, Han C Z 2002 Chin. Phys. 11 666
[5] Yu S M, Ma Z G, Qiu S S, Peng S G, Lin Q H 2004 Chin. Phys. 13 317
[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] Meng J, Wang X Y 2007 Acta Phys. Sin. 56 5142 (in Chinese) [孟 娟、王兴元 2007物理学报 56 5142]
[9] Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾、徐 伟 2007 物理学报 56 3101]
[10] Wang X Y, Wu X J 2007 Acta Phys. Sin. 56 1988 (in Chinese) [王兴元、武相军 2007 物理学报 56 1988]
[11] Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元、王明军 2007 物理学报 56 6843]
[12] Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 物理学报 57 4729]
[13] Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006 物理学报 55 6261]
[14] Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、黄娟娟 2006 物理学报 55 3997]
[15] Zhang H G, Zhao Y, Yu W, Yang D S 2008 Chin. Phys. B 17 4056
[16] Mainieri R, Rehacek J 1999 Phys. Rev. Lett.82 3042
[17] Li Z G, Xu D 2004 Chaos, Solitons and Fractals. 22 477
[18] Chee C Y, Xu D 2005 Chaos, Solitons and Fractals. 23 1063
[19] Wen G, Xu D 2005 Chaos, Solitons and Fractals. 26 71
[20] Hu M F, Xu Z Y, Zhang R 2008 Communications in Nonlinear Science and Numerical Simulation 13 456
[21] Lü J H, Chen G R 2002 International Journal of Bifurcation and Chaos. 12 659
[22] Wang X Y, Zhao G B 2010 International Journal of Modern Physics B 24 4619
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