Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronization of oscillators not sharing a common ground   Networks of coupled LC oscillators that do not share a common ground node are
studied. Both resistive coupling and inductive coupling are considered. For
networks under resistive coupling, it is shown that the oscillator-coupler
interconnection has to be bilayer if the oscillator voltages are to
asymptotically synchronize. Also, for bilayer architecture (when both resistive
and inductive couplers are present) a method is proposed to compute a
complex-valued effective Laplacian matrix that represents the overall coupling.
It is proved that the oscillators display synchronous behavior if and only if
the effective Laplacian has a single eigenvalue on the imaginary axis.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con