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arXiv · 1512.06140

Phase-locked Patterns of the Kuramoto Model on 3-Regular Graphs

Lee DeVille·Bard Ermentrout
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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 $π/2$.

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Lee DeVille, Bard Ermentrout. 2015-12-18. Phase-locked Patterns of the Kuramoto Model on 3-Regular Graphs. https://doi.org/10.1063/1.4961064

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