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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.9 P.1408~1413

http://doi.org/10.1631/jzus.2007.A1408


Nonlinear dynamics analysis of a new autonomous chaotic system


Author(s):  CHU Yan-dong, LI Xian-feng, ZHANG Jian-gang, CHANG Ying-xiang

Affiliation(s):  School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China; more

Corresponding email(s):   lixf1979@126.com

Key Words:  Lyapunov exponents, Bifurcation, Chaos, Phase space, Poincaré, sections


CHU Yan-dong, LI Xian-feng, ZHANG Jian-gang, CHANG Ying-xiang. Nonlinear dynamics analysis of a new autonomous chaotic system[J]. Journal of Zhejiang University Science A, 2007, 8(9): 1408~1413.

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author="CHU Yan-dong, LI Xian-feng, ZHANG Jian-gang, CHANG Ying-xiang",
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pages="1408~1413",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1408"
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%A CHANG Ying-xiang
%J Journal of Zhejiang University SCIENCE A
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1408

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T1 - Nonlinear dynamics analysis of a new autonomous chaotic system
A1 - CHU Yan-dong
A1 - LI Xian-feng
A1 - ZHANG Jian-gang
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J0 - Journal of Zhejiang University Science A
VL - 8
IS - 9
SP - 1408
EP - 1413
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1408


Abstract: 
In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or numerically, such as poincaré; map, lyapunov exponents and Lyapunov dimension. Based on this flow, a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[2] Chlouverakis, K.E., 2005. Color maps of the Kaplan-Yorke dimension in optically driven lasers: maximizing the dimension and almost-Hamiltonian chaos. Int. J. Bifurcat. & Chaos, 15:3011-3021.

[3] Chlouverakis, K.E., Adams, M.J., 2003. Stability maps of injection-locked laser diodes using the largest Lyapunov exponent. Opt. Commun., 216:405-412.

[4] Chlouverakis, K.E., Sprott, J.C., 2005. A comparison of correlation and Lyapunov dimensions. Physica D, 200:156-164.

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[6] Chua, L.O., Komuro, M., Matsum, T., 1986. The double scroll family. Part I: Rigorous proof of chaos. IEEE Trans. Circuits. Syst., 33:1072-1096.

[7] Frederickson, P., Kaplan, J.L., Yorke, E.D., 1983. The Lyapunov dimension of strange attractors. J. Differential Equations, 49:185-207.

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[10] Lorenz, E.N., 1963. Deterministic nonperiodic flow. J. Atmos. Sci., 20:130-141.

[11] Lü, J.H., Chen, G.R., 2002. A new chaotic attractor coined. Int. J. Bifurcat. & Chaos, 12(3):659-661.

[12] Rössler, O.E., 1976. An equation for continuous chaos. Phys. Lett. A, 57:397-398.

[13] Wieczorek, S., Krauskopf, B., Lenstra, D., 1999. A unifying view of bifurcations in a semiconductor laser subject to optical injection. Opt. Commun., 172:279-295.

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