Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase-locked Patterns of the Kuramoto Model on 3-Regular Graphs   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
$\pi/2$.

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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org