Information and entropy in strange attractors

Author

Fraser, Andrew M.

Author_Institution

Dept. of Phys., Texas Univ., Austin, TX, USA

Volume

35

Issue

2

fYear

1989

fDate

3/1/1989 12:00:00 AM

Firstpage

245

Lastpage

262

Abstract

A technique for analyzing time-series data from experiments is presented that provides estimates of four basic characteristics of a system: (1) the measure-theoretic entropy; (2) the accuracy of the measurements; (3) the number of measurements necessary to specify a system state; and (4) the best delay time T to use in order to construct phase space portraits by the method of delays. These characteristics are obtained by separating the entropy of measurements into a part due to noise and parts due to deterministic effects. For the technique to work, the noise associated with each measurement must be independent of the noise associated with all other measurements. An algorithm for implementing the analysis is presented with three examples

Keywords

chaos; entropy; information theory; time series; chaos; delay time; deterministic effects; entropy; information theory; measure-theoretic entropy; noise; phase space portraits; strange attractors; time-series data; Data analysis; Delay effects; Delay estimation; Entropy; Noise measurement; Phase estimation; Phase measurement; State estimation; Time measurement; Time series analysis;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.32121

Filename

32121