Affiliations: Instituto Militar de Engenharia, Department of
Mechanical and Materials Engineering, 22.290.270, Rio de Janeiro, RJ,
Brazil
Note: [] Address for correspondence: M.A. Savi, Universidade Federal do
Rio de Janeiro, COPPE – Department of Mechanical Engineering, 21.945.970 --
Rio de Janeiro, RJ, Brazil. E-mail: [email protected]
Abstract: 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.
Keywords: chaos, state space reconstruction, lyapunov exponents, time series
