Validity of Threshold-Crossing Analysis of Symbolic Dynamics from Chaotic Time Series

Erik M. Bollt, Theodore Stanford, Ying-Cheng Lai, and Karol Życzkowski
Phys. Rev. Lett. 85, 3524 – Published 16 October 2000
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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 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 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.

  • Received 4 May 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.3524

©2000 American Physical Society

Authors & Affiliations

Erik M. Bollt1, Theodore Stanford2, Ying-Cheng Lai3, and Karol Życzkowski4,5

  • 1Mathematics Department, 572 Holloway Road, U.S. Naval Academy, Annapolis, Maryland 21402-5002
  • 2Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001
  • 3Departments of Mathematics, Electrical Engineering, and Physics, Center for Systems Science and Engineering Research, Arizona State University, Tempe, Arizona 85287
  • 4Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059 Kraków, Poland
  • 5Centrum Fizyki Teoretycznej PAN, al. Lotników 32/46, 02-668 Warszawa, Poland

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Issue

Vol. 85, Iss. 16 — 16 October 2000

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