Abstract
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 denotes its adjacency matrix. Let the function be given by This function has a global maximum when θi = θ for all 1 ⩽ i ⩽ 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
