Transient chaotic behaviour versus periodic motion of a parametric pendulum by recurrence plots

G Litak, M Wiercigroch, B W Horton, X Xu

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

We investigated dynamic responses of a parametric pendulum obtained experimentally. Using the recurrence plot technique designed to analyze experimental time series we have distinguished different types of motion. This method, supplemented by recurrence quantification analysis (RQA), has been used to identify oscillations, rotations, and transient chaotic vibrations for relatively short time series composed of only few cycles.
Original languageEnglish
Pages (from-to)33-41
Number of pages9
JournalJournal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
Volume90
Issue number1
Early online date24 Nov 2009
DOIs
Publication statusPublished - Jan 2010

Fingerprint

Recurrence Plot
Transient Behavior
Periodic Motion
Pendulum
Pendulums
Chaotic Behavior
Time series
Recurrence Quantification Analysis
Dynamic Response
Dynamic response
Vibration
Oscillation
Cycle
Motion

Keywords

  • parametric pendulum
  • recurrence plot
  • chaotic vibration

Cite this

@article{0c637174d13b4aaaa7e46060cbce1ab4,
title = "Transient chaotic behaviour versus periodic motion of a parametric pendulum by recurrence plots",
abstract = "We investigated dynamic responses of a parametric pendulum obtained experimentally. Using the recurrence plot technique designed to analyze experimental time series we have distinguished different types of motion. This method, supplemented by recurrence quantification analysis (RQA), has been used to identify oscillations, rotations, and transient chaotic vibrations for relatively short time series composed of only few cycles.",
keywords = "parametric pendulum, recurrence plot, chaotic vibration",
author = "G Litak and M Wiercigroch and Horton, {B W} and X Xu",
year = "2010",
month = "1",
doi = "10.1002/zamm.200900290",
language = "English",
volume = "90",
pages = "33--41",
journal = "Journal of Applied Mathematics and Mechanics / Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik (ZAMM)",
issn = "0044-2267",
publisher = "WILEY-V C H VERLAG GMBH",
number = "1",

}

TY - JOUR

T1 - Transient chaotic behaviour versus periodic motion of a parametric pendulum by recurrence plots

AU - Litak, G

AU - Wiercigroch, M

AU - Horton, B W

AU - Xu, X

PY - 2010/1

Y1 - 2010/1

N2 - We investigated dynamic responses of a parametric pendulum obtained experimentally. Using the recurrence plot technique designed to analyze experimental time series we have distinguished different types of motion. This method, supplemented by recurrence quantification analysis (RQA), has been used to identify oscillations, rotations, and transient chaotic vibrations for relatively short time series composed of only few cycles.

AB - We investigated dynamic responses of a parametric pendulum obtained experimentally. Using the recurrence plot technique designed to analyze experimental time series we have distinguished different types of motion. This method, supplemented by recurrence quantification analysis (RQA), has been used to identify oscillations, rotations, and transient chaotic vibrations for relatively short time series composed of only few cycles.

KW - parametric pendulum

KW - recurrence plot

KW - chaotic vibration

U2 - 10.1002/zamm.200900290

DO - 10.1002/zamm.200900290

M3 - Article

VL - 90

SP - 33

EP - 41

JO - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)

JF - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)

SN - 0044-2267

IS - 1

ER -