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Characterizing synchronization in time series using information measures extracted from symbolic representations.

Roberto Monetti¹, Wolfram Bunk, Thomas Aschenbrenner

¹Max-Planck-Institut für Extraterrestrische Physik, 85748 Garching, Germany. monetti@mpe.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 13, 2009

Summary

This study introduces a novel symbolic method to analyze time series synchronization. The approach effectively characterizes coupled dynamics and assesses synchronization strength, even in noisy conditions.

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Area of Science:

Nonlinear dynamics
Time series analysis
Information theory

Background:

Characterizing synchronization in complex systems is crucial.
Existing methods may struggle with nonlinear dynamics or noise.
Symbolic representations offer a robust alternative for time series analysis.

Purpose of the Study:

To develop a new methodology for characterizing time series synchronization.
To utilize symbolic representations for analyzing coupled dynamics.
To assess the strength and robustness of synchronization measures.

Main Methods:

Mapping time series to symbolic sequences using p-dimensional delay vectors and rank-ordering.
Developing a transcription scheme for symbol comparison between time series.
Applying group-theoretical considerations and information measures for synchronization classification and strength assessment.
Testing the method on a prototype nonlinear system and evaluating robustness against noise.

Main Results:

The symbolic method successfully characterizes synchronization in a prototype nonlinear system.
A rich variety of coupled dynamics were revealed through symbolic analysis.
The proposed synchronization measure demonstrates robustness against noise.
Comparison with established measures highlights the advantages of the symbolic approach.

Conclusions:

The presented symbolic methodology provides a powerful tool for analyzing time series synchronization.
This approach offers a robust and versatile framework for understanding coupled dynamics in nonlinear systems.
The method's resilience to noise makes it suitable for real-world applications.