Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics

Liqiang Zhu, Ying-Cheng Lai, Frank C. Hoppensteadt, Erik M. Bollt

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Motivated by the practical consideration of the measurement of chaotic signals in experiments or the transmission of these signals through a physical medium, we investigate the effect of filtering on chaotic symbolic dynamics. We focus on the linear, time-invariant filters that are used frequently in many applications, and on the two quantities characterizing chaotic symbolic dynamics: topological entropy and bit-error rate. Theoretical consideration suggests that the topological entropy is invariant under filtering. Since computation of this entropy requires that the generating partition for defining the symbolic dynamics be known, in practical situations the computed entropy may change as a filtering parameter is changed. We find, through numerical computations and experiments with a chaotic electronic circuit, that with reasonable care the computed or measured entropy values can be preserved for a wide range of the filtering parameter.

Original languageEnglish (US)
Pages (from-to)410-419
Number of pages10
JournalChaos
Volume13
Issue number1
DOIs
StatePublished - Mar 2003

Fingerprint

Symbolic Dynamics
Chaotic Dynamics
Numerical Investigation
Experimental Investigation
Entropy
Filtering
entropy
Topological Entropy
Invariant
Numerical Computation
Error Rate
Linear Time
bit error rate
Bit error rate
Numerical Experiment
Partition
Electronics
Filter
partitions
Experiments

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics. / Zhu, Liqiang; Lai, Ying-Cheng; Hoppensteadt, Frank C.; Bollt, Erik M.

In: Chaos, Vol. 13, No. 1, 03.2003, p. 410-419.

Research output: Contribution to journalArticle

Zhu, Liqiang ; Lai, Ying-Cheng ; Hoppensteadt, Frank C. ; Bollt, Erik M. / Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics. In: Chaos. 2003 ; Vol. 13, No. 1. pp. 410-419.
@article{d61d216512e84634a041e99a4dbdde59,
title = "Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics",
abstract = "Motivated by the practical consideration of the measurement of chaotic signals in experiments or the transmission of these signals through a physical medium, we investigate the effect of filtering on chaotic symbolic dynamics. We focus on the linear, time-invariant filters that are used frequently in many applications, and on the two quantities characterizing chaotic symbolic dynamics: topological entropy and bit-error rate. Theoretical consideration suggests that the topological entropy is invariant under filtering. Since computation of this entropy requires that the generating partition for defining the symbolic dynamics be known, in practical situations the computed entropy may change as a filtering parameter is changed. We find, through numerical computations and experiments with a chaotic electronic circuit, that with reasonable care the computed or measured entropy values can be preserved for a wide range of the filtering parameter.",
author = "Liqiang Zhu and Ying-Cheng Lai and Hoppensteadt, {Frank C.} and Bollt, {Erik M.}",
year = "2003",
month = "3",
doi = "10.1063/1.1520090",
language = "English (US)",
volume = "13",
pages = "410--419",
journal = "Chaos (Woodbury, N.Y.)",
issn = "1054-1500",
publisher = "American Institute of Physics Publising LLC",
number = "1",

}

TY - JOUR

T1 - Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics

AU - Zhu, Liqiang

AU - Lai, Ying-Cheng

AU - Hoppensteadt, Frank C.

AU - Bollt, Erik M.

PY - 2003/3

Y1 - 2003/3

N2 - Motivated by the practical consideration of the measurement of chaotic signals in experiments or the transmission of these signals through a physical medium, we investigate the effect of filtering on chaotic symbolic dynamics. We focus on the linear, time-invariant filters that are used frequently in many applications, and on the two quantities characterizing chaotic symbolic dynamics: topological entropy and bit-error rate. Theoretical consideration suggests that the topological entropy is invariant under filtering. Since computation of this entropy requires that the generating partition for defining the symbolic dynamics be known, in practical situations the computed entropy may change as a filtering parameter is changed. We find, through numerical computations and experiments with a chaotic electronic circuit, that with reasonable care the computed or measured entropy values can be preserved for a wide range of the filtering parameter.

AB - Motivated by the practical consideration of the measurement of chaotic signals in experiments or the transmission of these signals through a physical medium, we investigate the effect of filtering on chaotic symbolic dynamics. We focus on the linear, time-invariant filters that are used frequently in many applications, and on the two quantities characterizing chaotic symbolic dynamics: topological entropy and bit-error rate. Theoretical consideration suggests that the topological entropy is invariant under filtering. Since computation of this entropy requires that the generating partition for defining the symbolic dynamics be known, in practical situations the computed entropy may change as a filtering parameter is changed. We find, through numerical computations and experiments with a chaotic electronic circuit, that with reasonable care the computed or measured entropy values can be preserved for a wide range of the filtering parameter.

UR - http://www.scopus.com/inward/record.url?scp=0037358820&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037358820&partnerID=8YFLogxK

U2 - 10.1063/1.1520090

DO - 10.1063/1.1520090

M3 - Article

C2 - 12675447

AN - SCOPUS:0037358820

VL - 13

SP - 410

EP - 419

JO - Chaos (Woodbury, N.Y.)

JF - Chaos (Woodbury, N.Y.)

SN - 1054-1500

IS - 1

ER -