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

E M Bollt, T Stanford, Y C Lai, K Zyczkowski, Ying-Cheng Lai

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57 Citations (Scopus)

Abstract

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 fur 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 a practice can lead 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.

Original languageEnglish
Pages (from-to)3524-3527
Number of pages4
JournalPhysical Review Letters
Volume85
Issue number16
Publication statusPublished - 16 Oct 2000

Keywords

  • MAP

Cite this

Bollt, E. M., Stanford, T., Lai, Y. C., Zyczkowski, K., & Lai, Y-C. (2000). Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series. Physical Review Letters, 85(16), 3524-3527.