  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 Roessler 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.
