Recurrence plots of experimental data: To embed or not to embed?

A recurrence plot is a visualization tool for analyzing experimental data. These plots often reveal correlations in the data that are not easily detec ted in the original time series. Existing recurrence plot analysis techniqu es, which are primarily application oriented and completely quantitative, r equire that the time-series data first be embedded in a high-dimensional sp ace, where the embedding dimension d(E) is dictated by the dimension d of t he data set, with d(E) greater than or equal to 2d + 1. One such set of rec urrence plot analysis tools, recurrence quantification analysis, is particu larly useful in finding locations in the data where the underlying dynamics change. We have found that for certain low-dimensional systems the same re sults can be obtained with no embedding. (C) 1998 American Institute of Phy sics. [S1054-1500(98)00604-1].