Adequate Sampling of a Chaotic Time Series.

摘要

Currently there is some disagreement about what constitutes an adequate sample of a time series with which chaos measures may be quantified. In this thesis, a method for objectively determining such a sample is presented. This method is based on a new, relatively efficient measure, the Histogram Measure, which allows large amounts of data to be considered. This measure also may be used to distinguish the chaotic from the transient, or nonchaotic, portions of the solution that are inherent in any chaotic time series. This is a crucial consideration, since transients contaminate the chaotic characteristics of any time series, be it from observations or models. This measure also leads to a predictability estimate--that of loss of information gain--as functions of sample length and elapsed time. The Histogram Measure is tested with time series generated by the Lorenz (1963) three-component model of Rayleigh-Benard convection. It is shown that the determination of criteria for quantifying adequate samples of data yields a definitive cost/benefit result. In effect, there is a balance between obtaining the greatest possible accuracy and spending the fewest resources; beyond a particular time or number of data points, only a minimal benefit is realized for the increased cost.