Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series

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.

12 pages single-spaced (total), 4 figures, 1 table

References in corpus (3)

• Stability ordering of cycle expansions
• Comment on "Optimal Periodic Orbits of Chaotic Systems"
• Computing the diffusion coefficient for intermittent maps: Resummation of stability ordered cycle expansions

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