Quantifying phase synchronization using instances of Hilbert phase slips

We propose to quantify phase synchronization between two signals, xt and yt, by calculating variance in the Hilbert phase of y(t) at instances of phase slips exhibited by xt. The proposed approach is tested on numerically simulated coupled chaotic Roessler systems and second order autoregressive processes. Furthermore we compare the performance of the proposed and original approaches using uterine electromyogram signals and show that both approaches yield consistent results A standard phase synchronization approach, which involves unwrapping the Hilbert phases (ϕ1t and ϕ2(t)) of the two signals and analyzing the variance in the |n⋅ϕ1t−m⋅ϕ2t|,mod2π, (n and m are integers), was used for comparison. The synchronization indexes obtained from the proposed approach and the standard approach agree reasonably well in all of the systems studied in this work. Our results indicate that the proposed approach, unlike the traditional approach, does not require the non-invertible transformations — unwrapping of the phases and calculation of mod2π and it can be used to reliably to quantify phase synchrony between two signals.