A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to...

Area of Science:

• Multidisciplinary science and engineering
• Complex systems analysis
• Dynamical systems theory

Background:

• Multichannel time series analysis is crucial for understanding complex systems.
• Characterizing synchrony in high-dimensional, nonlinear, nonstationary, and noisy systems is challenging.
• Complete synchronization is unlikely; phase synchronization is a more common phenomenon.

Purpose of the Study:

• To present a general method for analyzing multichannel time series.
• To quantify the degree of phase synchronization among channels.
• To provide insights into the fundamental dynamics of complex systems.

Main Methods:

• Calculating average phase-synchronization times from all channel pairs.
• Constructing a matrix of synchronization times.
• Developing a random-matrix based criterion to handle matrix singularity.
• Monitoring eigenvalues and determinant to assess synchrony changes.

Main Results:

• The proposed method effectively analyzes phase synchronization in complex systems.
• The random-matrix based criterion successfully addresses matrix singularity issues.
• The method was validated on a nonstationary noisy dynamical system and clinical EEG/ECoG data.

Conclusions:

• The developed method offers a powerful tool for assessing changes in synchrony in multichannel time series.
• This approach provides valuable insights into the dynamics of systems exhibiting phase synchronization.
• The technique is applicable to various scientific and engineering domains, including neuroscience.