Identification of deterministic chaos by an information-theoretic measure of the sensitive dependence on the initial conditions

Abstract

One of the most difficult problems in the field of non-linear time series analysis is the unequivocal characterization of a measured signal. We present a practicable procedure which allows to decide if a given time series is pure noise, chaotic but distorted by noise, purely chaotic, or a Markov process. Furthermore, the method gives an estimate of the Kolmogorov-Sinai (KS) entropy and the noise level. The procedure is based on a measure of the sensitive dependence on the initial conditions which is called ϵ-information flow. This measure generalizes the concept of KS entropy and characterizes the underlying dynamics. The ϵ-information flow is approximated by the calculation of various correlation integrals.