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Shock and Vibration
Volume 10, Issue 1, Pages 37-50

Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

L.F.P. Franca and M.A. Savi

Instituto Militar de Engenharia, Department of Mechanical and Materials Engineering, 22.290.270, Rio de Janeiro, RJ, Brazil

Received 14 November 2001; Revised 30 May 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.