Quantifying the dynamical complexity of time series

A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding cylinder sets. Quantitative estimates of the Kolmogorov-Sinai entropy are obtained by introducing a modified permutation entropy which takes into account the average width of the cylinder sets. The method works also in hyperchaotic systems and allows estimating the fractal dimension of the underlying attractors.