Information theory in non-linear dynamics and causality: State-space partition or ordinal patterns?

Area of Science:

• Nonlinear dynamics
• Information theory
• Time series analysis

Background:

• Information theory offers tools for analyzing complex systems.
• Quantifying coupling, causality, and complexity requires estimating probability distributions.
• Estimating these distributions from experimental data is challenging.

Purpose of the Study:

• To investigate the use of ordinal patterns as a method for analyzing time series.
• To explore replacing traditional state-space partitioning with symbolic encoding.
• To assess the applicability of ordinal patterns for information-theoretic measures.

Main Methods:

• Symbolic encoding of continuous time series data using ordinal patterns.
• Comparison with traditional state-space partitioning methods.
• Analysis of information-theoretic measures based on ordinal patterns.

Main Results:

• Ordinal patterns provide a viable alternative to state-space partitioning.
• Symbolic encoding simplifies the estimation of probability distributions.
• This approach facilitates the analysis of information transfer and entropy production.

Conclusions:

• Ordinal pattern analysis is a practical and effective method for time series analysis.
• It overcomes challenges associated with estimating multidimensional probability distributions.
• This technique enhances the application of information theory to nonlinear systems.