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. A symbol is linked to a sequence of numbers through the rank-order of its values. A representation of a time series results after mapping all sequences into symbols. We propose a transcription scheme between symbolic representations to study the dynamics of coupled systems. This scheme allows us to use elements of group theory and to derive information measures to assess the degree of synchronization. We apply our method to a prototype non-linear system which displays a rich coupled dynamics.