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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.4 P.296~304

http://doi.org/10.1631/jzus.2005.A0296


Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor


Author(s):  ALI M., SAHA L.M.

Affiliation(s):  Department of Mathematics, Faculty of Mathematical Science, Delhi University, Delhi 110007, India; more

Corresponding email(s):   mali_homs@yahoo.com

Key Words:  Chaotic attractor, Largest Lyapunov Exponent, Local Lyapunov Exponents


ALI M., SAHA L.M.. Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor[J]. Journal of Zhejiang University Science A, 2005, 6(4): 296~304.

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%I Zhejiang University Press & Springer
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T1 - Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor
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A1 - SAHA L.M.
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DOI - 10.1631/jzus.2005.A0296


Abstract: 
A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between local Lyapunov Exponents and the largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.

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

Reference

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[7] Kaplan, D., Glass, L., 1995. Understanding Non Linear Dynamics. In: Banchoff, T.F., Marsden, J., Ewing, J., Wagon, S., Gonnet, G. (Eds.), Textbooks in Mathematical Sciences. Springer-Verlag, New York, p.8-14.

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[9] Sandri, M., 1996. Numerical calculation of Lyapunov Exponents. The Mathematica Journal, 6(3):78-84.

[10] Wolf, A., Swift, J.B., Swenney, H.L., Vastano, J.A., 1985. Determining Lyapunov Exponents from a time series. Physica, 16D:285-317.

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