Quantifying interactions between complex oscillatory systems: a topic in time series analysis

This work is focused on the problem of identifying interactions between complex dynamical oscillatory processes. Discovering relationships in complex systems plays an important role in the process of understanding how subsystems cooperate to create complicated behavior. There are two main problems in interaction analysis: directionality analysis and synchronization detection. Synchronization is a process of mutual alignment of rhythms of two systems indicating a stronger form of cooperation. Directionality analysis is concerned with asymmetric interactions between systems and facilitates the discovery of drive-response relationships. Current frameworks for detecting synchronization and directionality are recounted, their properties are analyzed and new approaches to both problems are proposed. An experimental dataset is analyzed with the goal of describing changes in the human cardiorespiratory system between the waking state and general anesthesia. The proposed methods can be used in the context of nonlinear dynamics to investigate coupled biological, geological, meteorological, chemical and other types of process.