期刊
NONLINEARITY
卷 33, 期 11, 页码 5905-5918出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/ab9baa
关键词
synchronization; Kuramoto oscillator; energy landscape
资金
- National Science Foundation [DMS-1454939, CCF-1934964]
- NSF [DMS-1763179]
- Alfred P Sloan Foundation
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, letG= (V,E) be a connected graph and (a(ij))(i,j=1)(n) f:T-n -> R be given by f(theta(1), ..., ,theta(n))= Sigma(n)(i,j=1) cos(theta(i)-theta(j)). This function has a global maximum when theta(i) = theta for all 1 <= i <= n. It is known that if every vertex is connected to at least mu(n- 1) other vertices for mu sufficiently large, then every local maximum is global. Taylor proved this for mu >= 0.9395 and Ling, Xu & Bandeira improved this to mu > 0.7929. We give a slight improvement to mu >= 0.7889. Townsend, Stillman & Strogatz suggested that the critical value might be mu(c)= 0.75.
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