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Title: A highly specific test for periodicity

We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely, that the time series can be interpolated by a periodic function whose local extrema are also present in the time series. Our method is intended for the analysis of time series generated by deterministic time-continuous dynamical systems, where it can help telling periodic dynamics from chaotic or transient ones. We empirically investigate our method's performance and compare it to an approach based on marker events (or Poincaré sections). We demonstrate that our method is capable of detecting small deviations from periodicity and outperforms the marker-event-based approach in typical situations. Our method requires no adjustment of parameters to the individual time series, yields the period length with a precision that exceeds the sampling rate, and its runtime grows asymptotically linear with the length of the time series.
Authors:
 [1] ;  [2] ;  [2]
  1. Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn (Germany)
  2. (Germany)
Publication Date:
OSTI Identifier:
22482293
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 11; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; CHAOS THEORY; FUNCTIONS; LENGTH; PERFORMANCE; PERIODICITY; SAMPLING; TRANSIENTS