Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully re...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2000-05
Main Authors: Bollt, Erik M, Stanford, Theodore, Ying-Cheng, Lai, Zyczkowski, Karol
Format: Article
Language:English
Subjects:
Chaos theory
Dynamics
Entropy
Partitions
Time series
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such practice leads to a severe misrepresentation of the dynamical system. The measured topological entropy is a Devil's staircase-like, but surprisingly nonmonotone, function of a parameter characterizing the amount of misplacement of the partition.
ISSN:2331-8422
DOI:10.48550/arxiv.0005040