Reconstruction of phase-amplitude dynamics from signals of a network of oscillators

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.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — ProjectID 431549029, SFB 1451 and 491111487. GH was supported by PID-2021-122954NB-I00 funded by MCIN/AEI/ 10.13039/501100011033 and “ERDF: A way of making Europe”, the Maria de Maeztu Award for Centers and Units of Excellence in R&D (CEX2020-001084-M) and the AGAUR project 2021SGR1039.

Peer Reviewed

Postprint (author's final draft)