Symbolic Dynamics and Ordinal Time series Analysis

Dynamical systems can be considered on different levels of precision. For studying the qualitative behaviour of a system, it can be useful to choose a very coarse-grained description: The state space is divided into a small number of subregions, each coded by a symbol. In a discrete-time dynamical system, sequences of successive states of the system are turned into symbol sequences.

Symbolic dynamics studies dynamical systems on the base of the symbol sequences obtained for a suitable partition of the state space. It is also applied to the qualitative analysis of empirical time series. We focus on symbolic dynamics describing the ordinal structure of a system. Here we follow an idea of Bandt and Pompe, who have introduced the ordinal viewpoint into time series analysis. In particular, we describe EEG-based methods for detecting, visualizing and analyzing temporal and spatial qualitative changes of brain states related to epileptic activity.