A general nonlinear method to extract unstable periodic orbits from chaotic time series is proposed. By utilizing the estimated local dynamics along a trajectory, we devise a transformation of the time series data such that the transformed data are concentrated on the periodic orbits. Thus, one can extract unstable periodic orbits from a chaotic time series by simply looking for peaks in a finite grid approximation of the distribution function of the transformed data. Our method is demonstrated using data from both numerical and experimental examples, including neuronal ensemble data from mammalian brain slices. The statistical significance of the results in the presence of noise is assessed using surrogate data.

Original languageEnglish (US)
Pages (from-to)5398-5417
Number of pages20
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'Extracting unstable periodic orbits from chaotic time series data'. Together they form a unique fingerprint.

Cite this