Dynamical estimates of chaotic systems from Poincaré recurrences

M S Baptista, Dariel M Maranhão, J C Sartorelli

Research output: Contribution to journalArticle

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

Cite this

Dynamical estimates of chaotic systems from Poincaré recurrences. / Baptista, M S; Maranhão, Dariel M; Sartorelli, J C.

In: Chaos, Vol. 19, No. 4, 043115, 12.2009, p. 1-10.

Research output: Contribution to journalArticle

Baptista, MS, Maranhão, DM & Sartorelli, JC 2009, 'Dynamical estimates of chaotic systems from Poincaré recurrences', Chaos, vol. 19, no. 4, 043115, pp. 1-10. https://doi.org/10.1063/1.3263943
Baptista, M S ; Maranhão, Dariel M ; Sartorelli, J C. / Dynamical estimates of chaotic systems from Poincaré recurrences. In: Chaos. 2009 ; Vol. 19, No. 4. pp. 1-10.
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