Information-entropic analysis of chaotic time series: determination of time-delays and dynamical coupling

By calculating the conditional entropy of two different chaotic time series, converted into symbolic sequences through the application of prescribed (but otherwise arbitrary) rules, it can be determined whether or not these originate from the same underlying dynamics. We show that by comparing the conditional entropy of a sequence, obtained by coarse-graining of a chaotic time series, with respect to shifted copies of itself, time-delays that may be inherent in the dynamics can be found. Application is made to time-series obtained from dynamical systems such as Mackey–Glass equation and Ikeda equation. The method appears equally effective in determining the dynamical coupling of climatic time signals. Our results are robust to additive noise, and can thus be applied even when the conversion from a time series to a symbolic sequence has a small proportion of errors.