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The entrainment between weakly-coupled nonlinear oscillators, as well asbetween complex signals such as those representing physiological activity, isfrequently assessed in terms of whether a stable relationship is detectablebetween the instantaneous phases extracted from the measured or simulatedtime-series via the analytic signal. Here, we demonstrate that adding apossibly complex constant value to this normally null-mean signal has anon-trivial warping effect. Among other consequences, this introduces a levelof sensitivity to the amplitude fluctuations and average relative phase. Bymeans of simulations of Roessler systems and experiments on single-transistoroscillator networks, it is shown that the resulting coherence measure may havean empirical value in improving the inference of the structural couplings fromthe dynamics. When tentatively applied to the electroencephalogram recordedwhile performing imaginary and real movements, this straightforwardmodification of the phase locking value substantially improved theclassification accuracy. Hence, its possible practical relevance inbrain-computer and brain-machine interfaces deserves consideration.

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