Math @ Duke

Publications [#352858] of Jianfeng Lu
Papers Published
 Lu, J; Steinerberger, S, Synchronization of Kuramoto oscillators in dense networks,
Nonlinearity, vol. 33 no. 11
(November, 2020),
pp. 59055918 [doi]
(last updated on 2021/01/25)
Abstract: © 2020 IOP Publishing Ltd & London Mathematical Society Printed in the UK 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.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

