一个统一混沌系统及其研究

doi:10.7523/j.issn.2095-6134.2003.1.020

摘要/Abstract

摘要：

发现了一个新的混沌系统,它是介于著名的Lorenz系统和Chen系统之间的临界系统.同时,提出了一个单参数的统一混沌系统--Lorenz系统族,它包含Lorenz系统和Chen系统作为参数区间的两个极端系统,临界系统作为一个过渡系统.基于线性耦合多振子互同步问题的研究,提出了研究这一类问题的新方法--模式分解法,并首次从理论上给出了上述3个典型系统混沌同步的几个严格的充分条件.还提出了一类新的简单的切换分段线性反控制器,它能够使一个简单的线性系统在三维空间中同时产生n个,或一个具有多吸引域融合的复杂混沌吸引子.

关键词: Lorenz系统, Chen系统, 临界系统, 统一混沌系统, 混沌控制与同步

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

中图分类号:

O175

吕金虎, 陈关荣, 张锁春. 一个统一混沌系统及其研究[J]. 中国科学院大学学报, 2003, 20(1): 123-129.

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

参考文献

[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)