Abstract
We extend recent approaches based on the concept of phase synchronization to enable the time-resolved investigation of directional relationships between coupled dynamical systems from short and transient noisy time series. For our approach, we consider an observed ensemble of a sufficiently large number of time series as multiple realizations of a process. We derive an index that quantifies the direction of transient interactions and assess its statistical significance using surrogate techniques. Analysing time series from noisy and chaotic systems, we demonstrate numerically the applicability and limitations of our approach. Our findings from an exemplary application to event-related brain activities underline the importance of our method for improving knowledge about the mechanisms underlying memory formation in humans.
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