Suppose there are two nonlinear and non stationary time series what are the best and state of the art phase synchronization measures.
You can use an order parameter that measures the ratio between the time variance of the mean series and the mean of the time variances of the series. For time series Si(t), i=1,...,N
R = Vart ( Meani( Si ) / Meant ( Vart( Si) )
Meani(Si) is the mean over all time series
The order parameter R is between 0 and 1. If the times series are phased-synchronised, then Meani(Si) is close to any Si and the ratio R is close to 1. If the time series are out-of-phase, Meani(Si) is more or less constant and the numerator is small compared to the denominator: R is small.
https://www.researchgate.net/publication/8452190_Modeling_a_synthetic_multicellular_clock_repressilators_coupled_by_quorum_sensing_Proc_Natl_Acad_Sci_U_S_A
Article Modeling a synthetic multicellular clock: Repressilators cou...
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