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Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series

Scott M. Zoldi
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Abstract

Using the Lorenz equations, we have investigated whether unstable periodic orbits (UPOs) associated with a strange attractor may predict the occurrence of the robust sharp peaks in histograms of some experimental chaotic time series. Histograms with sharp peaks occur for the Lorenz parameter value r=60.0 but not for r=28.0, and the sharp peaks for r=60.0 do not correspond to any single histogram derived from a UPO. Despite this lack of correspondence, we show that histograms derived from a chaotic time series can be accurately predicted by an escape-time weighting of UPO histograms.

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Scott M. Zoldi. 1998-02-05. Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series. https://doi.org/10.1103/physrevlett.81.3375

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