Full Text:
<3102>
CLC number: O221
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 0
Clicked: 5524
Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor
| |||||||||||||
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.
@article{title="Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor",
author="ALI M., SAHA L.M.",
journal="Journal of Zhejiang University Science A",
volume="6",
number="4",
pages="296-304",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0296"
}
%0 Journal Article
%T Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor
%A ALI M.
%A SAHA L.M.
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 4
%P 296-304
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0296
TY - JOUR
T1 - Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor
A1 - ALI M.
A1 - SAHA L.M.
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 4
SP - 296
EP - 304
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
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.
[1] Chen, G., Dong, X., 1998. From Chaos to Order: Methodologies, Perspectives and Applications. In: Chua, L.O. (Ed.), Nonlinear Science. World Scientific Pub., Singapore, p.44-49.
[2] Drazin, P.G., 1992. Nonlinear Systems. Cambridge Univ. Press, Glasgow, p.233-246.
[3] Galias, Z., 1999. Local Transversal Lyapunov Exponents for analysis of synchronization of chaotic systems. Int. J. Circ. Theor. Appl., 27:589-604.
[4] Grond, F., Diebner, H.H., 2005. Local Lyapunov Exponents for dissipative continuous systems. Chaos, Solitons & Fractals, 23(5):1809-1817.
[5] Grond, F., Diebner, H.H., Sahle, S., Mathias, A., Fischer, S., Rossler, O.E., 2003. A robust, locally interpretable algorithm for Lyapunov Exponents. Chaos, Solitons & Fractals, 16(5):841-852.
[6] Henon, M., 1979. A two-dimensional mapping with strange attractor. Commun. Math. Phys., 50:69-77.
[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.
[8] Ott, E., Grebogi, C., Yorke, J., 1990. Controlling Chaotic Dynamical Systems. Chaos: Soviet-American Perspective on Nonlinear Science (American Institute of Physics, N.Y.), p.153-172.
[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.
Open peer comments: Debate/Discuss/Question/Opinion
<1>