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[1] Liu Wenbo, Chen Guanrong,. Compound structure analysis of a new chaotic system [J]. Journal of Southeast University (English Edition), 2004, 20 (4): 477-481. [doi:10.3969/j.issn.1003-7985.2004.04.017]
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Compound structure analysis of a new chaotic system()
一种新的混沌系统的复合结构分析
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 4
Page:
477-481
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2004-12-30

Info

Title:
Compound structure analysis of a new chaotic system
一种新的混沌系统的复合结构分析
Author(s):
Liu Wenbo1;  Chen Guanrong2
1College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China
刘文波;  陈关荣
南京航空航天大学自动化学院, 南京 210016) (香港城市大学电子工程系, 中国香港
Keywords:
three-dimensional autonomous system;  chaos;  equilibrium;  attractor;  characteristic equation;  compound structure
三维自治系统;  混沌;  平衡点;  吸引子;  特征方程;  复合结构
PACS:
O415.5
DOI:
10.3969/j.issn.1003-7985.2004.04.017
Abstract:
This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system. First, it is found that there exist five equilibria in the chaotic system, and the stabilities of these equilibria are discussed under a constant scalar control input parameter m. Secondly, the trajectories of the attractors on a y-z plane are examined, the reasons why these trajectories can exist or disappear are also described. Finally, the forming procedure of the different scrolls chaotic attractor is explored by computer simulations when the parameter m is varied. It is shown that the new chaotic attractor has a compound structure, it can evolve to other three-dimensional autonomous chaotic systems. The results of theoretical analysis and simulation are helpful for better understanding of other similar chaotic systems.
分析了一种新的三维自治混沌系统吸引子的复合结构. 首先证明了该混沌系统存在5个平衡点, 讨论了系统的控制参数大小同平衡点稳定性之间的关系. 其次, 对吸引子在y-z平面的运动轨迹作了理论分析, 描述了吸引子存在及消失的原因. 最后, 通过对该混沌系统运动轨迹在不同控制参数作用下的计算机仿真, 揭示了涡卷数不同的混沌吸引子形成的过程. 表明该混沌系统具有复合结构, 能够演化成其他的三维自治混沌系统. 理论分析及仿真结果对分析其他具有相似结构的混沌系统具有重要的参考价值.

References:

[1] Liu W B, Chen G. A new chaotic system and its generation [J]. International Journal of Bifurcation and Chaos, 2003, 13(1): 261-267.
[2] Liu W B, Chen G. Dynamical analysis of a 4-scroll chaotic attractor[J]. International Journal of Bifurcation and Chaos, 2004, 14(3): 971-998.
[3] Lü J, Chen G. Dynamical analysis of a new chaotic attractor [J]. International Journal of Bifurcation and Chaos, 2002, 12(5): 1001-1015.
[4] Nagle R K, Saff E B. Fundamentals of differential equations and boundary value problems [M]. New York: Addison Wesley, 1994.
[5] Liu W B, Chen G. Can a three-dimensional smooth autonomous quadratic chaotic system generate a single four-scroll attractor? [J]. International Journal of Bifurcation and Chaos, 2004, 14(4): 1395-1403.
[6] Lü J, Chen G, Zhang S. The compound structure of a new chaotic attractor [J]. Chaos Solitons and Fractals, 2002, 14(5): 669-672.
[7] Lü J, Zhou T, Chen G, et al. The compound structure of Chen’s attractor [J]. International Journal of Bifurcation and Chaos, 2002, 12(4): 855-858.
[8] Elwakil A, Kennedy M P. Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices [J]. IEEE Trans Circuits Syst — Ⅰ, 2001, 48(3): 289-307.
[9] Ozoguz S, Elwakil A, Kennedy M P. Experimental verification of the butterfly attractor in a modified Lorenz system [J]. IEEE Trans Circuits Syst — Ⅰ, 2002, 49(4): 527-530.

Memo

Memo:
Biography: Liu Wenbo(1968—), female, associate professor, wenboliu@nuaa.edu.cn.
Last Update: 2004-12-20