Work

The random graph process is globally synchronizing

Year: 2025

Type: article

Abstract: The homogeneous Kuramoto model on a graph is a network of identical oscillators, one at each vertex, where every oscillator is coupled bidirectionally (with unit strength) to its neighbors in the graph. A graph is said to be globally synchronizing if, for almost every initial condition, the homogeneous Kuramoto model converges to the all‐in‐phase synchronous state. Confirming a conjecture of Abdalla, Bandeira, Kassabov, Souza, Strogatz, and Townsend, we show that with high probability, the random graph process becomes globally synchronizing as soon as it is connected. This is best possible, since connectivity is a necessary condition for global synchronization.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70226

Authors: Vishesh Jain, Clayton Mizgerd, Mehtaab Sawhney

Institutions: University of Illinois Chicago, Columbia University

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: National Science Foundation, Clay Mathematics Institute