Estimation of delay in coupling from time series

Abstract

We demonstrate that a time delay in weak coupling between two self-sustained oscillators can be estimated from the observed time series data. We present two methods which are based on the analysis of interrelations between the phases of the signals. We show analytically and numerically that irregularity of the phase dynamics (due to the intrinsic noise or chaos) is essential for determination of the delay. We compare and contrast both methods to the standard cross-correlation analysis.