Counting Equilibria of the Kuramoto Model Using Birationally Invariant Intersection Index | Zendy

Tianran Chen | Zendy; Robert Davis | Zendy; Dhagash Mehta | Zendy

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Counting Equilibria of the Kuramoto Model Using Birationally Invariant Intersection Index

Author(s) -

Tianran Chen,

Robert Davis,

Dhagash Mehta

Publication year - 2018

Publication title -

siam journal on applied algebra and geometry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.052

H-Index - 15

ISSN - 2470-6566

DOI - 10.1137/17m1145665

Subject(s) - invariant (physics) , intersection (aeronautics) , kuramoto model , mathematics , upper and lower bounds , synchronization (alternating current) , algebraic number , computer science , discrete mathematics , topology (electrical circuits) , combinatorics , mathematical analysis , engineering , aerospace engineering , mathematical physics

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.

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