High-Order Phase Reduction for Coupled Oscillators
Abstract
We explore the phase reduction in networks of coupled oscillators in the higher orders of the coupling parameter. For coupled Stuart-Landau oscillators, where the phase can be introduced explicitly, we develop an analytic perturbation procedure to allow for the obtaining of the higher-order approximation explicitly. We demonstrate this by deriving the second-order phase equations for a network of three Stuart-Landau oscillators. For systems where explicit expressions of the phase are not available, we present a numerical procedure that constructs the phase dynamics equations for a small network of coupled units. We apply this approach to a network of three van der Pol oscillators and reveal components in the coupling with different scaling in the interaction strength.
Cite
@article{arxiv.2007.14077,
title = {High-Order Phase Reduction for Coupled Oscillators},
author = {Erik Genge and Erik Teichmann and Michael Rosenblum and Arkady Pikovsky},
journal= {arXiv preprint arXiv:2007.14077},
year = {2020}
}