Characterizing synchronization in time series using information measures extracted from symbolic representations

We present a methodology to characterize synchronization in time series based on symbolic representations. Each time series is mapped onto a sequence of p-dimensional delay vectors that are subsequently transformed into symbols by means of a rank-ordering of their values. Based on these representations, we propose a transcription scheme between symbols of the respective time series to study synchronization properties. Group-theoretical considerations and the use of information measures allow us to classify regimes of synchronization and to assess its strength. We apply our method to a prototype nonlinear system, which reveals a rich variety of coupled dynamics. We investigate in detail the robustness of the derived synchronization measure against noise and compare its value with that of the established measures.