Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory

Xing Pei, Kevin Dolan, Frank Moss, Ying-Cheng Lai

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The experimental detection of unstable periodic orbits in dynamical systems, especially those which yield short, noisy or nonstationary data sets, is a current topic of interest in many research areas. Unfortunately, for such data sets, only a few of the lowest order periods can be detected with quantifiable statistical accuracy. The primary observable is the number of encounters the general trajectory has with a particular orbit. Here we show that, in the limit of large period, this quantity scales exponentially with the period, and that this scaling is robust to dynamical noise. (C) 1998 American Institute of Physics. [S1054-1500(98)00904-5].

Original languageEnglish
Pages (from-to)853-860
Number of pages8
JournalChaos
Volume8
Issue number4
DOIs
Publication statusPublished - Dec 1998

Keywords

  • low-dimensional dynamics
  • time-series
  • strange sets
  • topological analysis
  • plateau onset
  • attractors
  • biology
  • occur
  • laws

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