Synchronization of Kuramoto oscillators in dense networks
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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- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics