Three Formulations of the Kuramoto Model as a System of Polynomial Equations
arXiv:1603.05905
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.
References in corpus (6)
- Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis
- Phase transitions and topology changes in configuration space
- Enumerating Gribov copies on the lattice
- Exploring the energy landscape of XY models
- On a microcanonical relation between continuous and discrete spin models
- Power Flow as an Algebraic System