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 journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)853-860
Number of pages8
JournalChaos
Volume8
Issue number4
DOIs
StatePublished - Dec 1998
Externally publishedYes

ASJC Scopus subject areas

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

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