Dynamics analysis and synchronization of T chaotic system with its circuit simulation

Wang Zhen; Sun Wei

doi:10.7498/aps.62.020511

Abstract

The stability of equilibrium of a T chaotic system is analyzed, and the system bifurcation, Lyapunov exponent, Poincare section with numerical analysis are studied. Also, the synchronization problem with T chaotic systems with known or unknown parameters is studied in this paper. According to the Lyapunov function, feedback controller of the system is designed and has been proved. An electronic circuit is designed to realize the controller using Multisim. The simulation results demonstrate the effectiveness and realizableness of the proposed method.

Keywords:

Authors and contacts

Wang Zhen¹,
Sun Wei^1,2

1.
Department of Foundation, Xijing University, Xi'an 710123, China;
2.
School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10971164), the Natural Science Foundation of Shaanxi Province (Grant No. 2011EJ001), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant Nos. 12JK1077, 12JK1073), and the Scientific Research Foundation of Xijing University (Grant Nos. XJ120107, XJ120108).

References

[1]	Lorenz E N 1963 Journal of the Atmospheric Sciences 20 130
[2]	Chen G, Ueta T 1999 International Journal of Bifurcation and Chaos 9 1465
[3]	Vanecek A, Celikovsky S 1996 Control systems: From linear analysis to synthesis of chaos, London, Prentice-Hall
[4]	L J, Chen G 2002 International Journal of Bifurcation and Chaos 12 659
[5]	Celikovsky S, Chen G 2002 International Journal of Bifurcation and Chaos 12 1789
[6]	Yang Q G, Chen G R 2008 International Journal of Bifurcation and Chaos 18 1393
[7]	Li W D, Wang X Y 2009 Techniques of Automation and Applications 28 1 (in Chinese) [李卫东, 王秀岩 2009 自动化技术与应用 28 1]
[8]	Han J H, Wu Y J 2006 Computer Simulation 23 6 (in Chinese) [韩军海, 吴云洁 2006 计算机仿真 23 6]
[9]	Wang Z, Wu Y T, Li Y X, Zou Y J 2009 Proceedings of the 4th ICCSE 441
[10]	Wang Z 2011 Control Theory & Applications 28 1036 (in Chinese) [王震 2011 控制理论与应用 28 1036]
[11]	Wang Z 2007 Analysis in Theory and Applications 23 343
[12]	Wang Z, Li Y X, Xi X J 2011 Acta Phys. Sin. 60 010513 (in Chinese) [王震, 李永新, 惠小健 2011 物理学报 60 010513]
[13]	Sprott J C 1994 Phys. Rev.E 50 647
[14]	Wei Z C 2011 Physics Letters A 376 102
[15]	Wei Z C, Yang Q G 2012 Nonlinear Dynamics 68 543
[16]	Wang Z 2010 Nonlinear Dynamics 60 369
[17]	Gh. Tigan 2005 Scientific Bulletin of the politehnica University of Timisoara 50 61
[18]	Li C G, Chen G R 2004 Chaos, Solitons & Fractals 22 549
[19]	Lu J J, Liu C X 2007 Chin. Phys. 16 1586
[20]	Xu Z, Liu C X 2008 Chin. Phys. B 17 4033

Cited By

[1]	Lorenz E N 1963 Journal of the Atmospheric Sciences 20 130
[2]	Chen G, Ueta T 1999 International Journal of Bifurcation and Chaos 9 1465
[3]	Vanecek A, Celikovsky S 1996 Control systems: From linear analysis to synthesis of chaos, London, Prentice-Hall
[4]	L J, Chen G 2002 International Journal of Bifurcation and Chaos 12 659
[5]	Celikovsky S, Chen G 2002 International Journal of Bifurcation and Chaos 12 1789
[6]	Yang Q G, Chen G R 2008 International Journal of Bifurcation and Chaos 18 1393
[7]	Li W D, Wang X Y 2009 Techniques of Automation and Applications 28 1 (in Chinese) [李卫东, 王秀岩 2009 自动化技术与应用 28 1]
[8]	Han J H, Wu Y J 2006 Computer Simulation 23 6 (in Chinese) [韩军海, 吴云洁 2006 计算机仿真 23 6]
[9]	Wang Z, Wu Y T, Li Y X, Zou Y J 2009 Proceedings of the 4th ICCSE 441
[10]	Wang Z 2011 Control Theory & Applications 28 1036 (in Chinese) [王震 2011 控制理论与应用 28 1036]
[11]	Wang Z 2007 Analysis in Theory and Applications 23 343
[12]	Wang Z, Li Y X, Xi X J 2011 Acta Phys. Sin. 60 010513 (in Chinese) [王震, 李永新, 惠小健 2011 物理学报 60 010513]
[13]	Sprott J C 1994 Phys. Rev.E 50 647
[14]	Wei Z C 2011 Physics Letters A 376 102
[15]	Wei Z C, Yang Q G 2012 Nonlinear Dynamics 68 543
[16]	Wang Z 2010 Nonlinear Dynamics 60 369
[17]	Gh. Tigan 2005 Scientific Bulletin of the politehnica University of Timisoara 50 61
[18]	Li C G, Chen G R 2004 Chaos, Solitons & Fractals 22 549
[19]	Lu J J, Liu C X 2007 Chin. Phys. 16 1586
[20]	Xu Z, Liu C X 2008 Chin. Phys. B 17 4033

[1]	Zhou Xiao-Yong. A novel chaotic system and its circuit simulation. Acta Physica Sinica, 2012, 61(3): 030504. doi: 10.7498/aps.61.030504
[2]	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
[3]	Huang Li-Lian, Xin Fang, Wang Lin-Yu. Circuit implementation and control of a new fractional-order hyperchaotic system. Acta Physica Sinica, 2011, 60(1): 010505. doi: 10.7498/aps.60.010505
[4]	Li Xiu-Chun, Gu Jian-Hua, Wang Yun-Lan, Zhao Tian-Hai. Observer synchronization method for a class of perturbed chaotic systems with unknown parameters. Acta Physica Sinica, 2011, 60(3): 030505. doi: 10.7498/aps.60.030505
[5]	Zhang Ruo-Xun, Yang Shi-Ping. Chaos in the fractional-order conjugate Chen system and its circuit emulation. Acta Physica Sinica, 2009, 58(5): 2957-2962. doi: 10.7498/aps.58.2957
[6]	Tang Liang-Rui, Li Jing, Fan Bing, Zhai Ming-Yue. A new three-dimensional chaotic system and its circuit simulation. Acta Physica Sinica, 2009, 58(2): 785-793. doi: 10.7498/aps.58.785
[7]	Liu Ling, Su Yan-Chen, Liu Chong-Xin. A new chaotic system and its circuit simulation. Acta Physica Sinica, 2007, 56(4): 1966-1970. doi: 10.7498/aps.56.1966
[8]	Luo Run-Zi. Impulsive control and synchronization of a new chaotic system. Acta Physica Sinica, 2007, 56(10): 5655-5660. doi: 10.7498/aps.56.5655
[9]	Wang Fan-Zhen, Qi Guo-Yuan, Chen Zeng-Qiang, Zhang Yu-Hui, Yuan Zhu-Zhi. Analysis, circuit implementation and synchronization of a new three-dimensional chaotic system. Acta Physica Sinica, 2006, 55(8): 4005-4012. doi: 10.7498/aps.55.4005
[10]	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
[11]	Ma Wen-Qi, Yang Cheng-Hui. Hopf bifurcation from synchronous chaos and its circuit simulation in a coupled nonlinear oscillator system. Acta Physica Sinica, 2005, 54(3): 1064-1070. doi: 10.7498/aps.54.1064
[12]	Li Shi-Hua, Cai Hai-Xing. Research on circuitry realization and synchronization of Chen chaotic systems. Acta Physica Sinica, 2004, 53(6): 1687-1693. doi: 10.7498/aps.53.1687
[13]	Zhou Ping. Observers for a class of 3D continuous chaotic systems. Acta Physica Sinica, 2003, 52(5): 1108-1111. doi: 10.7498/aps.52.1108
[14]	Guan Xin-Ping, He Yan-Hui, Wu Jing. Synchronization in chaotic systems based on resilient controller. Acta Physica Sinica, 2003, 52(11): 2718-2722. doi: 10.7498/aps.52.2718
[15]	Guan Xin-Ping, He Yan-Hui, Fan Zheng-Ping. Synchronization of a class of chaotic systems in the presence of perturbation by an observer. Acta Physica Sinica, 2003, 52(2): 276-280. doi: 10.7498/aps.52.276
[16]	Yue Dong, Jun Yoneyama. Adaptive fuzzy synchronization of chaotic systems with uncertainties. Acta Physica Sinica, 2003, 52(2): 292-297. doi: 10.7498/aps.52.292
[17]	Lu Zhi-Gang, Yu Ling-Hui, Liu Xiao-Jing, Gao Mei-Jing, Wu Shi-Chang. . Acta Physica Sinica, 2002, 51(10): 2211-2215. doi: 10.7498/aps.51.2211
[18]	GUAN XIN-PING, FAN ZHENG-PING, PENG HAI-PENG, WANG YI-QUN. THE SYNCHRONIZATION OF CHAOTIC SYSTEMS BASED ON RBF NETWORK IN THE PRESENCE OF PERTURBATION. Acta Physica Sinica, 2001, 50(9): 1670-1674. doi: 10.7498/aps.50.1670
[19]	GUAN XIN-PING, TANG YING-GAN, FAN ZHENG-PING, WANG YI-QUN. NEURAL NERWORK BASED ROBUST ADAPTIVE SYNCHRONIZATION OF A CHAOTIC SYSTEM. Acta Physica Sinica, 2001, 50(11): 2112-2115. doi: 10.7498/aps.50.2112
[20]	YANG XIAO-SONG. OBSERVERS FOR A CLASS OF CHAOTIC SYSTEMS. Acta Physica Sinica, 2000, 49(10): 1919-1921. doi: 10.7498/aps.49.1919

Catalog

Vol. 62, Issue 2 - 2013-01-20

Metrics

Abstract views: 7684
PDF Downloads: 640
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