# Synchronization of Kuramoto oscillators in dense networks

Journal Article (Journal Article)

We study synchronization properties of systems of Kuramoto oscillators. The problem can also be understood as a question about the properties of an energy landscape created by a graph. More formally, let G = (V, E) be a connected graph and (a ) = denotes its adjacency matrix. Let the function f : T → R n be given by f(θ , . . ., θ ) = P a cos(θ − θ ). This function has a global i, j=1 maximum when θ = θ for all 1 6 i 6 n. It is known that if every vertex is connected to at least µ(n − 1) other vertices for µ sufficiently large, then every local maximum is global. Taylor proved this for µ > 0.9395 and Ling, Xu & Bandeira improved this to µ > 0.7929. We give a slight improvement to µ > 0.7889. Townsend, Stillman & Strogatz suggested that the critical value might be µ = 0.75. i j i , j 1 1 n i j i j i c n n

### Full Text

### Duke Authors

### Cited Authors

- Lu, J; Steinerberger, S

### Published Date

- November 1, 2020

### Published In

### Volume / Issue

- 33 / 11

### Start / End Page

- 5905 - 5918

### Electronic International Standard Serial Number (EISSN)

- 1361-6544

### International Standard Serial Number (ISSN)

- 0951-7715

### Digital Object Identifier (DOI)

- 10.1088/1361-6544/ab9baa

### Citation Source

- Scopus