Influence of nonlinear amplitude dynamics on estimated delay time of coupling between self-oscillatory systems

The well-known method of estimating the delay time of coupling between self-oscillatory systems on the basis of their time series is based on empirical modeling of the observed phase dynamics by a system of first-order phase oscillators under the assumption that amplitude fluctuations can be ignored. We have studied the applicability of this method in the presence of significant amplitude fluctuations caused by an external noise or the chaotic dynamics of oscillators. Numerical experiments with systems of standard coupled oscillators show that the method under consideration gives incorrect estimations in some situations. A diagnostics of these situations is proposed, and modification of the estimator that eliminates errors is described and justified.