A new hyperchaotic system and its adaptive tracking control

Li Chun-Lai; Yu Si-Min

doi:10.7498/aps.61.040504

Abstract

In this paper, a four-dimensional hyperchaotic system is constructed by adding a state feedback controller into a chaotic system. Numerical simulations and theoretical analysis show that this four-dimensional system will take on periodic,complex periodic, quasi-periodic chaotic hyperchaotic dynamical behaviours as parameters vary. Moreover, an electronic circuit diagram is designed for demonstrating the existence of the hyperchaos. Finally, an adaptive tracking controller is proposed to acquire adaptive tracking control for this hyperchaotic system.

Keywords:

Authors and contacts

Li Chun-Lai^1,2,
Yu Si-Min¹

1.
College of Automation,Guangdong University of Technology, Guangzhou 510006, China;
2.
College of Physics and Electronics, Hunan Institute of Science and Technology, Yueyang 414006, China
Funds: Project supported by the National Natural Science Foundation of China(Grant Nos.60572073,60871025), and the Natural Science Foundation of Guangdong Province(Grant Nos.8151009001000060, 8351009001000002).

References

[1]	Lorenz E N 1963 J. Atmospheric Sci. 20 130
[2]	Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. CAS 33 1072
[3]	Chen G R, Ueta T 1999 Internat. J. Bifur. Chaos 9 1465
[4]	Lü J H, Chen G R 2002 Intenat. J. Bifur. Chaos 12 695
[5]	Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[6]	Zhou P, Wei L, Cheng X 2009 Chin. Phys. B 18 2674
[7]	Si G Q, Cao H, Zhang Y B 2011 Chin. Phys. B 20 010509
[8]	Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 100501
[9]	Bao B C, Liu Z, Xu J P and Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成, 刘中, 许建平, 朱雷 2010 59 1540]
[10]	Yang Q G, Chen G R 2008 Internat. J. Bifur. Chaos 18 1393
[11]	Liu C X, Liu T, Liu K, Liu L 2004 Chaos,Solitons Fract. 22 1031

Cited By

[1]	Lorenz E N 1963 J. Atmospheric Sci. 20 130
[2]	Chua L O, Komuro M, Matsumoto T 1986 IEEE Trans. CAS 33 1072
[3]	Chen G R, Ueta T 1999 Internat. J. Bifur. Chaos 9 1465
[4]	Lü J H, Chen G R 2002 Intenat. J. Bifur. Chaos 12 695
[5]	Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[6]	Zhou P, Wei L, Cheng X 2009 Chin. Phys. B 18 2674
[7]	Si G Q, Cao H, Zhang Y B 2011 Chin. Phys. B 20 010509
[8]	Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 100501
[9]	Bao B C, Liu Z, Xu J P and Zhu L 2010 Acta Phys. Sin. 59 1540 (in Chinese) [包伯成, 刘中, 许建平, 朱雷 2010 59 1540]
[10]	Yang Q G, Chen G R 2008 Internat. J. Bifur. Chaos 18 1393
[11]	Liu C X, Liu T, Liu K, Liu L 2004 Chaos,Solitons Fract. 22 1031

[1]	Ma Tie-Dong, Jiang Wei-Bo, Fu Jie, Xue Fang-Zheng. Synchronization of hyperchaotic systems via improved impulsive control method. Acta Physica Sinica, 2012, 61(10): 100507. doi: 10.7498/aps.61.100507
[2]	Bao Bo-Cheng, Hu Wen, Xu Jian-Ping, Liu Zhong, Zou Ling. Analysis and implementation of memristor chaotic circuit. Acta Physica Sinica, 2011, 60(12): 120502. doi: 10.7498/aps.60.120502
[3]	Li Nong, Li Jian-Fen, Liu Yu. Tracking control and parameters identification of a class of chaotic systems with unknown parameters. Acta Physica Sinica, 2011, 60(5): 050507. doi: 10.7498/aps.60.050507
[4]	Zhou Xiao-Yong. A chaotic system with invariable Lyapunov exponent and its circuit simulation. Acta Physica Sinica, 2011, 60(10): 100503. doi: 10.7498/aps.60.100503
[5]	Liu Yang-Zheng, Lin Chang-Sheng, Wang Zhong-Lin. A new switched four-scroll hyperchaotic system and its circuit implementation. Acta Physica Sinica, 2010, 59(12): 8407-8413. doi: 10.7498/aps.59.8407
[6]	Yu Si-Yao, Guo Shu-Xu, Gao Feng-Li. Calculation of the Lyapunov exponent for low frequency noise in semiconductor laser and chaos indentification. Acta Physica Sinica, 2009, 58(8): 5214-5217. doi: 10.7498/aps.58.5214
[7]	Zhang Xiao-Dan, Liu Xiang, Zhao Pin-Dong. Methods for calculating the main-axis Lyapunov exponents of a type of chaotic systems with delay. Acta Physica Sinica, 2009, 58(7): 4415-4420. doi: 10.7498/aps.58.4415
[8]	Zhang Yong, Guan Wei. Predication of multivariable chaotic time series based on maximal Lyapunov exponent. Acta Physica Sinica, 2009, 58(2): 756-763. doi: 10.7498/aps.58.756
[9]	Li Chun-Lai, Luo Xiao-Shu. Tracking control and projective synchronization in the fifth-order hyperchaotic circuit system based on accelerated factor. Acta Physica Sinica, 2009, 58(6): 3759-3764. doi: 10.7498/aps.58.3759
[10]	Liu Ming-Hua, Feng Jiu-Chao. A new hyperchaotic system. Acta Physica Sinica, 2009, 58(7): 4457-4462. doi: 10.7498/aps.58.4457
[11]	Liu Yang-Zheng, Jiang Chang-Sheng. Building and analysis of properties of a class of correlative and switchable hyperchaotic system. Acta Physica Sinica, 2009, 58(2): 771-778. doi: 10.7498/aps.58.771
[12]	Tang Liang-Rui, Li Jing, Fan Bing. A new four-dimensional hyperchaotic system and its circuit simulation. Acta Physica Sinica, 2009, 58(3): 1446-1455. doi: 10.7498/aps.58.1446
[13]	Min Fu-Hong, Yu Yang, Ge Cao-Jun. Circuit implementation and tracking control of the fractional-order hyper-chaotic Lü system. Acta Physica Sinica, 2009, 58(3): 1456-1461. doi: 10.7498/aps.58.1456
[14]	Min Fu-Hong, Wang Zhi-Quan. Generalized projective synchronization and tracking control of complex Dynamos systems. Acta Physica Sinica, 2008, 57(1): 31-36. doi: 10.7498/aps.57.31
[15]	. Tracking control of Lorenz systems in unidirectional coupling network. Acta Physica Sinica, 2007, 56(12): 6851-6856. doi: 10.7498/aps.56.6851
[16]	Chen Long, Wang De-Shi. Adaptive tracking control of the Chen system. Acta Physica Sinica, 2007, 56(10): 5661-5664. doi: 10.7498/aps.56.5661
[17]	Liu Yang-Zheng, Jiang Chang-Sheng, Lin Chang-Sheng, Sun Han. Four-dimensional switchable hyperchaotic system. Acta Physica Sinica, 2007, 56(9): 5131-5135. doi: 10.7498/aps.56.5131
[18]	Li Jian-Fen, Lin Hui, Li Nong. Chaotic synchronization with diverse structures based on tracking control. Acta Physica Sinica, 2006, 55(8): 3992-3996. doi: 10.7498/aps.55.3992
[19]	Wang Xing-Yuan, Shi Qi-Jiang. Tracking control and synchronization of the R?ssler's chaotic system. Acta Physica Sinica, 2005, 54(12): 5591-5596. doi: 10.7498/aps.54.5591
[20]	LI LI-XIANG, PENG HAI-PENG, LU HUI-BIN, GUAN XIN-PING. CONTROL AND SYNCHRONIZATION OF HéNON CHAOTIC SYSTEM. Acta Physica Sinica, 2001, 50(4): 629-632. doi: 10.7498/aps.50.629

Catalog

Vol. 61, Issue 4 - 2012-02-20

Metrics

Abstract views: 9426
PDF Downloads: 917
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板