# Chaotic Data: Delay Time and Embedding Dimension

Chaotic Data: Delay Time and Embedding Dimension

This Demonstration shows how to determine the delay time and embedding dimension for four datasets (each of length 4000). The data is derived from the logistic, Hénon and Lorenz models and NMR laser data. The delay time can be inferred from the average mutual information at various time lags: the suitable delay time is the time lag for which there is a local minimum in the average mutual information. Or, if a local minimum does not exist, the time lag at which the first substantial decrease in the average mutual information has occurred.

The phase portrait also helps to define the delay time: the suitable value is when the phase portrait reveals the presence of a strange attractor. In this case, the extension of the attractor in all space dimensions is roughly the same, and the attractor can be seen to more or less fill the embedding space. The embedding dimension can be inferred from fractions of false nearest neighbors: the suitable embedding dimension is that for which the fraction of false nearest neighbors has dropped to zero (or nearly zero).