A parametrisation method for high-order phase reduction in coupled oscillator networks
Dynamical Systems
2023-06-07 v1
Abstract
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic expansion for an embedding of the perturbed invariant torus, as well as for the reduced phase dynamics in local coordinates. Both can be determined to arbitrary degrees of accuracy, and we show that the phase dynamics may directly be obtained in normal form. We apply the method to predict remote synchronisation in a chain of coupled Stuart-Landau oscillators.
Cite
@article{arxiv.2306.03320,
title = {A parametrisation method for high-order phase reduction in coupled oscillator networks},
author = {Sören von der Gracht and Eddie Nijholt and Bob Rink},
journal= {arXiv preprint arXiv:2306.03320},
year = {2023}
}
Comments
29 pages, 3 figures