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

Research output: Contribution to journalArticle

58 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.

Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series. / Bollt, E M ; Stanford, T ; Lai, Y C ; Zyczkowski, K ; Lai, Ying-Cheng.

In: Physical Review Letters, Vol. 85, No. 16, 16.10.2000, p. 3524-3527.

Research output: Contribution to journalArticle

Bollt, EM, Stanford, T, Lai, YC, Zyczkowski, K & Lai, Y-C 2000, 'Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series', Physical Review Letters, vol. 85, no. 16, pp. 3524-3527.
Bollt EM, Stanford T, Lai YC, Zyczkowski K, Lai Y-C. Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series. Physical Review Letters. 2000 Oct 16;85(16):3524-3527.
Bollt, E M ; Stanford, T ; Lai, Y C ; Zyczkowski, K ; Lai, Ying-Cheng. / Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series. In: Physical Review Letters. 2000 ; Vol. 85, No. 16. pp. 3524-3527.
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