Analysing Time Series using Symbolic Representations

摘要

We present a method 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 is obtained af-ter 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 informa-tion measures to assess the degree of synchronization. We apply our method to a prototype non-linear system which displays a rich coupled dynamics.