[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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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

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

Keywords:

three-dimensional autonomous system;  chaos;  equilibrium;  attractor;  characteristic equation;  compound structure

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.

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.

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