title: Oscillating systems with cointegrated phase processes.
abstract: We present cointegration analysis as a method to infer the network structure of a linearly phase coupled oscillating system. By defining a class of oscillating systems with interacting phases, we derive a data generating process where we can specify the coupling structure of a network that resembles biological processes. In particular we study a network of Winfree oscillators, for which we present a statistical analysis of various simulated networks, where we conclude on the coupling structure: the direction of feedback in the phase processes and proportional coupling strength between individual components of the system. We show that we can correctly classify the network structure for such a system by cointegration analysis, for various types of coupling, including uni-/bi-directional and all-to-all coupling. Finally, we analyze a set of EEG recordings and discuss the current applicability of cointegration analysis in the field of neuroscience.
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark. ostergaard@math.ku.dk.
authors.forename: Jacob
authors.identifier: 0000-0002-0969-4016
authors.initials: J
authors.lastname: Østergaard
authors.affiliation: Department of Economics, University of Copenhagen, Øster Farimagsgade 5, Building 26, 1353, Copenhagen K, Denmark.
authors.forename: Anders
authors.initials: A
authors.lastname: Rahbek
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen Ø, Denmark.
authors.forename: Susanne
authors.initials: S
authors.lastname: Ditlevsen
mesh_terms: D003198:Computer Simulation; D004569:Electroencephalography / Q000706:statistics & numerical data; D058407:Electroencephalography Phase Synchronization / Q000502:physiology; D025461:Feedback, Physiological; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D010507:Periodicity
keywords: Cointegration; Coupled oscillators; EEG signals; Interacting dynamical system; Phase process; Synchronization; Winfree oscillator