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Updated: May 10, 2025

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
Published on: May 25, 2019
Reconstruction of phase-amplitude dynamics from signals of a network of oscillators
Azamat Yeldesbay1,2, Gemma Huguet3,4, Silvia Daun1,2
1Cognitive Neuroscience, Institute of Neuroscience and Medicine (INM-3), Research Centre Jülich, Jülich, Germany.
Abstract:
We present a novel method of reconstructing the phase-amplitude dynamics directly from signals of a network of oscillators to estimate the coupling between its nodes. For this purpose, we use the recent advances in the field of phase-amplitude reduction of oscillatory systems, which allow the representation of an uncoupled oscillatory system as a phase-amplitude oscillator in a unique form using transformations (parameterizations) related to the eigenfunctions of the Koopman operator. By combining the parameterization method and the Fourier-Laplace averaging method for finding the eigenfunctions of the Koopman operator, we developed a method of assessing the transformation functions from the signals of the interacting oscillatory systems. The resulting reconstructed dynamical system is a network of phase-amplitude oscillators with the interactions between them represented as coupling functions in phase and amplitude coordinates.
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