Dynamical estimates of chaotic systems from Poincaré recurrences

M S Baptista, Dariel M Maranhão, J C Sartorelli

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5 Citations (Scopus)

Abstract

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov–Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Hénon map and experimentally in a Chua’s circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications.
Original languageEnglish
Article number043115
Pages (from-to)1-10
Number of pages10
JournalChaos
Volume19
Issue number4
DOIs
Publication statusPublished - Dec 2009

Keywords

  • unstable periodic-orbits
  • kolmogorov-entropy
  • time statistics
  • return times
  • attractors
  • series

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