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 has angle difference greater than $\pi /2$.

References in corpus (2)

• Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis
• The spectral index of signed Laplacians and their structural stability

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