Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series
type: Item
instance of: scholarly article
title: Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series
zbMATH Open document ID: 1230.37015
DOI: 10.1080/10260220290013507
author: A. M. López Jiménez
author: C. Camacho Martínez-Vara de Rey
author: A. R. García Torres
published in: Discrete Dynamics in Nature and Society
publication date: 2012-01-23T00:00:00Z
review text: Summary: 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 \(\lambda \) 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.
Mathematics Subject Classification ID: 37A50
Mathematics Subject Classification ID: 37M10
zbMATH DE Number: 5999611
zbMATH Keywords: non-linear dynamics
zbMATH Keywords: attractor
zbMATH Keywords: chaos
zbMATH Keywords: Lyapunov exponent
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1080/10260220290013507
OpenAlex ID: W2021232820
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description: scientific article; zbMATH DE number 5999611