Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series

Details Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series Unstable Periodic Orbit Analysis of Histograms of Chaotic Time Series

1998-02-05

arxiv.org/abs/chao-dyn/9802005v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevLett.81.3375

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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