Interval estimates of coupling delay using time series of oscillators

Estimation of Characteristics of Delayed Coupling Between Stochastic Oscillators from the Observed Phase Dynamics

“…The dependence S 2 k (Δ j→k , a k ) and its minimum value s 2 k (Δ j→k ) = min a k S 2 k (Δ j→k , a k ) for the fixed Δ j→k are considered in [21] for estimating the delay time. The quantity s 2 k (Δ j→k ) is minimized as a function of the test delay Δ j→k (see Fig.…”

“…The well-known method [21] is based on the construction of an empirical model of the phase dynamics of the observed processes x 1 (t) and x 2 (t). To this end, using the available time series x 1 (t) and x 2 (t) and one of the well-known methods (e.g., see [22]), we calculate the time series {φ 1 (t 1 ), .…”

“…This estimation is based on empirical simulation of the phase dynamics with allowance for the influence of the phase-noise intensity on the estimation error. The efficiency of this estimation was demonstrated for the systems subject to white noise [21]. However, the noise properties in the phase dynamics can often be different, as in the case of small-size chaotic systems [22], e.g., the Rössler system in the regime of phase-coherent chaos [22,23], and nonautonomous systems subject to the random-signal action.…”

“…Since it is important to control the estimation errors during the analysis of relatively short noisy signals, an interval estimation of the delay time of coupling among the oscillatory systems using the time series was proposed in [21]. This estimation is based on empirical simulation of the phase dynamics with allowance for the influence of the phase-noise intensity on the estimation error.…”

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“…Для оценки значимости могут использованы как традиционные варианты усреднений, так и аналитические оценки значимости и устранения ошибок, связанных со статистическими особенностями временных рядов. Одна из модификаций этой методики, использованную в данной работе, включает интервальную оценку ошибки прогноза [9]. Отдельно следует отметить, что чувствительность к высокочастотным шумам не является недостатком этого метода из-за того, что сигналы исследуемых систем приходится фильтровать полосовым фильтром [6].…”