Phase dynamics modeling technique for estimation of delayed couplings between nonlinear oscillators accounting for influence of amplitudes

An established interval estimator of a time delay in coupling between oscillators, which is based on empirical modeling of phase dynamics and maximum likelihood formalism, is shown to give sometimes erroneous conclusions about the value of the time delay. It occurs when the dynamics of amplitudes affects phases, which is typical of nonlinear oscillatory systems under the influence of strong noises or in chaotic regimes. We suggest an empirical criterion to diagnose such situations and a modified estimator of time delay which allows one to avoid erroneous conclusions. Both approaches are applied to the estimation of couplings between climate processes El-Nino/Southern Oscillation and North Atlantic Oscillation from observational data.