title: Phase-locked patterns of the Kuramoto model on 3-regular graphs.
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.
authors: Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801, USA.
authors: Lee
authors: L
authors: DeVille
authors: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, Pennsylvania 15260, USA.
authors: Bard
authors: B
authors: Ermentrout