统一超混沌系统的投影同步

阿布都热合曼·卡的尔; 王兴元; 赵玉章

doi:10.7498/aps.60.040506

摘要

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性.

关键词:

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.

Keywords:

unified hyperchaotic system /
adaptive control /
full state hybrid projective synchronization /
active control

作者及机构信息

(1)大连理工大学电子信息与电气工程学部,大连 116024; (2)大连理工大学电子信息与电气工程学部,大连 116024;新疆财经大学计算机科学与工程学院,乌鲁木齐 830012; (3)新疆财经大学计算机科学与工程学院,乌鲁木齐 830012

基金项目: 国家自然科学基金(批准号:60973152,60573172),高等学校博士学科点专项科研基金(批准号:20070141014 ) 和辽宁省自然科学基金(批准号:20082165)资助的课题.

Authors and contacts

(1)Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China; (2)Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China;School of Computer Science and Engineering, Xinjiang University of Finance and Economics, Urumchi 830012, China; (3)School of Computer Science and Engineering, Xinjiang University of Finance and Economics, Urumchi 830012, China

参考文献

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[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 56 3803]
[8]	Meng J, Wang X Y 2007 Acta Phys. Sin. 56 5142 (in Chinese) [孟娟、王兴元 2007 56 5142]
[9]	Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾、徐伟 2007 56 3101]
[10]	Wang X Y, Wu X J 2007 Acta Phys. Sin. 56 1988 (in Chinese) [王兴元、武相军 2007 56 1988]
[11]	Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元、王明军 2007 56 6843]
[12]	Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 57 4729]
[13]	Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006 55 6261]
[14]	Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、黄娟娟 2006 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

施引文献

[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 56 3803]
[8]	Meng J, Wang X Y 2007 Acta Phys. Sin. 56 5142 (in Chinese) [孟娟、王兴元 2007 56 5142]
[9]	Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾、徐伟 2007 56 3101]
[10]	Wang X Y, Wu X J 2007 Acta Phys. Sin. 56 1988 (in Chinese) [王兴元、武相军 2007 56 1988]
[11]	Wang X Y, Wang M J 2007 Acta Phys. Sin. 56 6843 (in Chinese) [王兴元、王明军 2007 56 6843]
[12]	Liu F C, Song J Q 2008 Acta Phys. Sin. 57 4729 (in Chinese) [刘福才、宋佳秋 2008 57 4729]
[13]	Wu X J, Wang X Y 2006 Acta Phys. Sin. 55 6261 (in Chinese) [武相军、王兴元 2006 55 6261]
[14]	Cai G L, Huang J J 2006 Acta Phys. Sin. 55 3997 (in Chinese) [蔡国梁、黄娟娟 2006 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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