Delay time window and plateau onset of the correlation dimension for small data sets

作者：H. S. Kim, R. Eykholt, José D. Salas · 发表于：Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 年份：1998 · DOI：10.1103/physreve.58.5676 · 被引用次数：40 · 研究领域：Complex Systems and Time Series Analysis、Chaos control and synchronization、Theoretical and Computational Physics

The method of delays is widely used for reconstructing chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\ensuremath{\tau}}_{d}$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\ensuremath{\tau}}_{w}$ instead. Unfortunately, ${\ensuremath{\tau}}_{w}$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\ensuremath{\tau}}_{w}$ has yet emerged. However, the recently introduced $C\ensuremath{-}C$ method can be used to estimate either ${\ensuremath{\tau}}_{d}$ or ${\ensuremath{\tau}}_{w}.$ Using this method, we show that, for small data sets, fixing ${\ensuremath{\tau}}_{w},$ rather than ${\ensuremath{\tau}}_{d},$ does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m is increased.