Three Formulations of the Kuramoto Model as a System of Polynomial Equations
Optimization and Control
2019-09-24 v2 Systems and Control
Algebraic Geometry
Chaotic Dynamics
Abstract
We compare three formulations of stationary equations of the Kuramoto model as systems of polynomial equations. In the comparison, we present bounds on the numbers of real equilibria based on the work of Bernstein, Kushnirenko, and Khovanskii, and performance of methods for the optimisation over the set of equilibria based on the work of Lasserre, both of which could be of independent interest.
Keywords
Cite
@article{arxiv.1603.05905,
title = {Three Formulations of the Kuramoto Model as a System of Polynomial Equations},
author = {Tianran Chen and Jakub Marecek and Dhagash Mehta and Matthew Niemerg},
journal= {arXiv preprint arXiv:1603.05905},
year = {2019}
}