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Warped phase coherence: an empirical synchronization measure combining phase and amplitude information. (English) Zbl 1409.34051
Summary: The entrainment between weakly coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the instantaneous phases extracted from the measured or simulated time-series via the analytic signal. Here, we demonstrate that adding a possibly complex constant value to this normally null-mean signal has a non-trivial warping effect. Among other consequences, this introduces a level of sensitivity to the amplitude fluctuations and average relative phase. By means of simulations of Rössler systems and experiments on single-transistor oscillator networks, it is shown that the resulting coherence measure may have an empirical value in improving the inference of the structural couplings from the dynamics. When tentatively applied to the electroencephalogram recorded while performing imaginary and real movements, this straightforward modification of the phase locking value substantially improved the classification accuracy. Hence, its possible practical relevance in brain-computer and brain-machine interfaces deserves consideration.
©2019 American Institute of Physics
MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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