Estimation of the coupling delay time from time series of self-oscillatory systems with allowance for the autocorrelation function of phase noise

We propose to determine the delay time of coupling between self-oscillatory systems using a modification of the well-known method based on a model of the oscillation phase dynamics, which ensures its applicability in the case of nonwhite noises influencing this dynamics. For this purpose, the method of calculating a confidence interval is refined by allowance for the correlation time of the phase noise. The applicability of the proposed estimator is illustrated by the results of numerical experiments with systems of standard coupled oscillators.