Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic synchronization under all three types of coupling: position,
  velocity, and acceleration   Synchronization of identical harmonic oscillators interconnected via
position, velocity, and acceleration couplings is studied. How to construct a
complex Laplacian matrix representing the overall coupling is presented. It is
shown that the oscillators asymptotically synchronize if and only if this
matrix has a single eigenvalue on the imaginary axis. This result generalizes
some of the known spectral tests for synchronization. Some simpler Laplacian
constructions are also proved to work provided that certain structural
conditions are satisfied by the coupling graphs.

37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga