Three Formulations of the Kuramoto Model as a System of Polynomial Equations
For researchers studying the Kuramoto model, this work offers a theoretical comparison of algebraic formulations, but it is incremental as it applies known techniques without demonstrating practical improvements.
The paper compares three polynomial formulations of the Kuramoto model's stationary equations, providing bounds on the number of real equilibria and evaluating optimization methods over the equilibrium set. No concrete performance numbers are reported.
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.