A Unified Chaotic System and Its Research

doi:10.7523/j.issn.2095-6134.2003.1.020

Abstract

Abstract:

Produces a new chaotic system, which is a critical system betweem the Lorenz andChen systems. At the same time, we introduce a unified chaotic system with single parameter,called Lorenz system families, which contains the Lorenz and the Chen systems as two dualsystems at the two extremes of its parameter spectrum, and acritical system as a transitionsystem. Based on the study of the chaos synchronization between linearly coupled multi-sys-tems, presents a new method mode decomposition for analyzing the stability of synchroni-zation solution, some sufficient conditions for synchronization are gained from rigorouslymathematical analysis for the first time. Finally, Introduces several new chaos generators,switching piecewise-linear controllers, which can create simultaneously n, or one with multi-ple merged basins of attraction chaotic attractors from a 3-D linear system within a wide rangeof parameter values.

Key words: Lorenz system, Chen system, critical system, unified chaotic system, chaos con-trol and synchronization

CLC Number:

O175

L Jinhu, Chen Guanrong, Zhang Suochun. A Unified Chaotic System and Its Research[J]. , 2003, 20(1): 123-129.

References

[1] Chen G, Dong X. From Chaos to Order: Methodologies, Perspectives and Applications. Singapore: World Scientific, 1998

[2] Lü J, Lu J, Chen S. Chaotic Time Series Analysis and Its Application. Wuhan: Wuhan University Press, 2002 (in Chinese)

[3] Chen G, Lü J. Dynamical Analysis, Control and Symchronization of the Generalized Lorenz Systems Family. Beijing: Science Press 2003 (in Chinese)

[4] Chen G, Ueta T. Yet another chaotic attractor. Int J Bifurcation Chaos, 1999, 9(7): 1465~1466

[5] Lü J, Chen G, A new chaotic attractor coined. Int J Bifurcation Chaos, 2002, 12(3): 659~661

[6] Lü J, Chen G, Zhang S. Dynamical analysis of a new chaotic attractor. Int J Bifurcation Chaos, 2002, 12(5): 1001~1015

[7] Lü J, ZhouT, ChenG, ZhangS. The compound structure of Chen' s attractor. Int J Bifurcation Chaos, 2002, 12(4): 855~858

[8] Lü J, Chen G, Zhang S. Controlling in between the Lorenz and the Chen systems. Int J Bifurcation Chaos, 2002, 12(6): 1417~1422

[9] Lü J, ZhouT, ChengG, ZhangS. Local bifurcation of the Chen system. IntJBifurcationChaos, 2002, 12(10): 2257~2270

[10] Lü J, Chen G, Cheng D, Celikovsky S. Bridge the gap between the Lorenz system and the Chen system. Int J Bifurcation Chaos,2002, 12(12): accepted

[11] Lü J, Zhou T, Chen G, Yang X. Generating chaos with a switching piecewise-linear controller. Chaos, 2002, 12(2): 344~349

[12] Lü J, Chen G, Yu X. Generating chaotic attractors with multiple merged basins of attraction: A switching piecewise-linear contro approach. IEEE Trans Circuits Syst I, 2002: accepted

[13] Lü J, Zhang S. Controlling Chen' s chaotic attractor using backstepping design based on parameters identification. Phys Lett A,2001, 256:148~152

[14] Lü J, Zhou T, Zhang S. Chaos synchronization between linearly coupled chaotic system. Chaos, Solitons and Fractals, 2002, 14(4): 529~541

[15] Lü J, Chen G, Zhang S. The compound structure of a new chaotic attractor. Chaos, Solitons and Fractals, 2002, 14(5): 669~672

[16] Chen S, Lü J. Synchronization of an uncertain unified chaotic system via adaptive control. Chaos, Solitons and Fractals, 2002, 14(4): 643~647

[17] Lü J, Chen G, Yu Y. Asymptotic analysis of a modified Lorenz system. Chin Phys Lett, 2002, 19(9): 1260~1263

[18] Lu J, Lü J, Xie J, Chen G. On reconstruction of the Lorenz and Chen systems with noisy observation. Comput Math Appl, 2002,accepted

[19] Tao C, Lu J, Lü J, Liu M. The parameter identification and tracking of a unified system. Chin Phys Lett, 2002, 19(5): 632~635

[20] Lü J, Zhou T, Zhang S. Controlling Chen's chaotic attractor using feedback function based on parameters identification. Chin Phys, 2002, 11(1): 12~16

[21] Zhou T, Lü J, Chen G, Tang Y. Synchronization stability of three chaotic systems with linear coupling. Phys Lett A, 2002, 301:231~240

[22] Chen S, Lü J. Parameters identication and synchronization of chaotic systems based on adaptive control. Phys Lett A, 2002, 299(4)353~358

[23] Lü J, Lu J. Controlling uncertain Lü system using linear feedback. Chaos, Soliton and Fractals, 2003, accepted

[24] Chen S, Liu J, Feng J, Lü J. Synchronizing chaotic systems in strict-feedback form using a single controller. Chin Phys Lett, 2002,19(5): 1257~1259

[25] Lu J, Wu X, Lü J. Synchronization of a unified chaotic system and the application in secure communication. Phys Lett A, 2002. accepted

[26] Vanecek A, Celikovsky S. Control Systems: From Linear Analysis to Synthesis of Chaos. London: Prentice-Hall, 1996

[27] Yu Y, Zhang S. Controlling uncertain Lü system using backstepping design. Chaos, Solitons and Fractals, 2003, 15: 897~902

[28] Zhou Z. A new chaotic anti-control model--Lü system. J Xianning Teachers College, 2002, 22:19~21 (in Chinese)