Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronization of harmonic oscillators under restorative coupling with
  applications in electrical networks   The role of restorative coupling on synchronization of coupled identical
harmonic oscillators is studied. Necessary and sufficient conditions, under
which the individual systems' solutions converge to a common trajectory, are
presented. Through simple physical examples, the meaning and limitations of the
theorems are expounded. Also, to demonstrate their versatility, the results are
extended to cover LTI passive electrical networks. One of the extensions
generalizes the well-known link between the asymptotic stability of the
synchronization subspace and the second smallest eigenvalue of the Laplacian
matrix.

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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom