Quantifying the Dynamical Complexity of Chaotic Time Series.

Abstract

A powerful approach is proposed for the characterization of chaotic signals. It is based on the combined use of two classes of indicators: (i)the probability of suitable symbolic sequences (obtained from the ordinal patterns of the corresponding time series); (ii)the width of the corresponding cylinder sets. This way, much information can be extracted and used to quantify the complexity of a given signal. As an example of the potentiality of the method, I introduce a modified permutation entropy which allows for quantitative estimates of the Kolmogorov-Sinai entropy in hyperchaotic models, where other methods would be unpractical. As a by-product, estimates of the fractal dimension of the underlying attractors are possible as well.