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 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 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

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Catalog

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

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