Characterizing dynamical transitions by statistical complexity measures based on ordinal pattern transition networks.

Area of Science:

• Nonlinear dynamics
• Complex systems analysis
• Time series analysis

Background:

• Traditional time series analysis methods often miss complex features.
• Complex network approaches offer novel insights into nonlinear dynamics.
• Ordinal pattern transition networks are an emerging technique for time series characterization.

Purpose of the Study:

• To generalize statistical complexity measures (SCMs) by incorporating ordinal pattern transition frequencies.
• To enhance the characterization of time series data using a novel network approach.
• To demonstrate the effectiveness of generalized SCMs in identifying dynamical transitions.

Main Methods:

• Application of ordinal pattern transition networks to time series data.
• Generalization of traditional statistical complexity measures (SCMs) based on permutation entropy.
• Analysis of dynamical transitions in the logistic map and real-world experimental data (fluid dynamics, ECG).

Main Results:

• Generalized SCMs effectively characterize dynamical transitions in both artificial and real-world time series.
• Incorporating transition frequencies between ordinal patterns yields dynamically meaningful complexity estimates.
• The proposed method reveals features often hidden by traditional analysis techniques.

Conclusions:

• Ordinal pattern transition networks provide a powerful framework for advanced time series analysis.
• Generalized SCMs offer a promising tool for analyzing observational data, particularly in complex systems.
• This approach enhances the understanding of nonlinear dynamics and system behavior through detailed pattern transition analysis.