Warped phase coherence: An empirical synchronization measure combining phase and amplitude information

Area of Science:

• Nonlinear dynamics and complex systems
• Signal processing and time-series analysis
• Neuroscience and biomedical engineering

Background:

• Assessing entrainment in nonlinear oscillators and physiological signals typically relies on instantaneous phases derived from analytic signals.
• Current methods may be sensitive to amplitude fluctuations and average relative phase, potentially limiting accurate coupling inference.
• The standard approach uses a null-mean signal for phase extraction.

Purpose of the Study:

• To investigate the effect of adding a complex constant to the normally null-mean signal used for phase extraction.
• To explore how this modification impacts the assessment of entrainment and coupling in nonlinear systems and physiological data.
• To evaluate the potential of this modified approach for improving brain-computer and brain-machine interfaces.

Main Methods:

• Simulations using Rössler systems to model coupled nonlinear oscillators.
• Experiments on single-transistor oscillator networks to validate findings.
• Application to electroencephalogram (EEG) data recorded during imaginary and real movements.

Main Results:

• Adding a complex constant introduces a non-trivial warping effect on the instantaneous phase.
• This modification increases sensitivity to amplitude fluctuations and average relative phase.
• The modified coherence measure demonstrated improved inference of structural couplings from dynamics in simulations and experiments.
• Application to EEG data significantly enhanced classification accuracy for real and imaginary movements.

Conclusions:

• A straightforward modification to phase extraction by adding a complex constant offers a valuable tool for analyzing coupled nonlinear systems.
• This approach enhances the detection of system couplings and improves the performance of brain-computer interfaces.
• The practical relevance of this method in brain-computer and brain-machine interfaces warrants further consideration and development.