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Discrete Dynamics in Nature and Society
Volume 7, Issue 1, Pages 41-52

Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

1Department of Experimental Psychology, University of Seville, Avda. Camilo José Cela s/n. 41005 Seville, Spain
2physics Seminar, I.E.S. Los Viveros, Avda. Blas Infante, s/n. Seville, Spain

Received 21 April 2001

Copyright © 2002 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.


The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.