On the detection of determinism in a time series
type: Item
instance of: scholarly article
title: On the detection of determinism in a time series
zbMATH Open document ID: 0942.37054
DOI: 10.1016/S0167-2789(99)00033-0
author: Yanyan Li
published in: Physica D
publication date: 2000-08-21T00:00:00Z
review text: The authors propose a simple and numerically robust method for differentiating chaotic dynamics from stochastic dynamics which is of special importance in the study of aperiodic and apparently irregular signals. This cannot be done by conventional spectral analysis since both chaos and random signals have continuous broadband power spectra. But as the nonlinear theory of dynamical systems shows, a chaotic process would have a finite dimensional attractor whereas a truly random process would be infinitely large dimensional. In order to work out the difference the nonlinear scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with the derivate from its surrogate counterpart. Relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process indicates chaoticity. The proposed method is based on singular value decomposition which is often used for the characterization of chaotic dynamics. In contrast to earlier works on the subject the sets of normalized orthogonal modes generated are mutually nonlinearly related and the energy distribution in each set of orthogonal modes of the data matrix is nonlinearly scaled.
Mathematics Subject Classification ID: 37M10
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 1370241
zbMATH Keywords: time series
zbMATH Keywords: bifurcation diagrams
zbMATH Keywords: determinism
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: singular value decomposition
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1370241