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Synchronization of Kuramoto oscillators in dense networks

Publication ,  Journal Article
Lu, J; Steinerberger, S
Published in: Nonlinearity
November 1, 2020

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 (ai j)ni, j=1 denotes its adjacency matrix. Let the function f : Tn → R n be given by f(θ1, . . ., θn) = P ai j cos(θi − θ j). This function has a global i, j=1 maximum when θi = 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 µc = 0.75.

Duke Scholars

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Published In

Nonlinearity

DOI

EISSN

1361-6544

ISSN

0951-7715

Publication Date

November 1, 2020

Volume

33

Issue

11

Start / End Page

5905 / 5918

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Lu, J., & Steinerberger, S. (2020). Synchronization of Kuramoto oscillators in dense networks. Nonlinearity, 33(11), 5905–5918. https://doi.org/10.1088/1361-6544/ab9baa
Lu, J., and S. Steinerberger. “Synchronization of Kuramoto oscillators in dense networks.” Nonlinearity 33, no. 11 (November 1, 2020): 5905–18. https://doi.org/10.1088/1361-6544/ab9baa.
Lu J, Steinerberger S. Synchronization of Kuramoto oscillators in dense networks. Nonlinearity. 2020 Nov 1;33(11):5905–18.
Lu, J., and S. Steinerberger. “Synchronization of Kuramoto oscillators in dense networks.” Nonlinearity, vol. 33, no. 11, Nov. 2020, pp. 5905–18. Scopus, doi:10.1088/1361-6544/ab9baa.
Lu J, Steinerberger S. Synchronization of Kuramoto oscillators in dense networks. Nonlinearity. 2020 Nov 1;33(11):5905–5918.
Journal cover image

Published In

Nonlinearity

DOI

EISSN

1361-6544

ISSN

0951-7715

Publication Date

November 1, 2020

Volume

33

Issue

11

Start / End Page

5905 / 5918

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics