Counting equilibria of the Kuramoto model using birationally invariant intersection index
Algebraic Geometry
2017-08-31 v1 Combinatorics
Abstract
Synchronization in networks of interconnected oscillators is a fascinating phenomenon that appear naturally in many independent fields of science and engineering. A substantial amount of work has been devoted to understanding all possible synchronization configurations on a given network. In this setting, a key problem is to determine the total number of such configurations. Through an algebraic formulation, for tree and cycle graphs, we provide an upper bound on this number using the birationally invariant intersection index of a system of rational functions on a toric variety.
Keywords
Cite
@article{arxiv.1708.09246,
title = {Counting equilibria of the Kuramoto model using birationally invariant intersection index},
author = {Tianran Chen and Robert Davis and Dhagash Mehta},
journal= {arXiv preprint arXiv:1708.09246},
year = {2017}
}