Dynamical estimates of chaotic systems from Poincaré recurrences

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...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2009-12, Vol.19 (4), p.043115-043115-10
Main Authors: Baptista, M. S., Maranhão, Dariel M., Sartorelli, J. C.
Format: Article
Language:English
Subjects:
Algorithms
Computer Simulation
Models, Statistical
Nonlinear Dynamics
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Summary: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.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.3263943