Phase-locked patterns of the Kuramoto model on 3-regular graphs
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Published on: January 28, 2019
Lee DeVille1, Bard Ermentrout2
1Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801, USA.
Abstract:
We consider the existence of non-synchronized fixed points to the Kuramoto model defined on sparse networks: specifically, networks where each vertex has degree exactly three. We show that "most" such networks support multiple attracting phase-locked solutions that are not synchronized and study the depth and width of the basins of attraction of these phase-locked solutions. We also show that it is common in "large enough" graphs to find phase-locked solutions where one or more of the links have angle difference greater than π/2.
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