Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sync: Persistence in Two Diffusively Coupled Oscillators   We address the problem of stability of synchronization in two diffu- sively
coupled oscillators under small perturations. We have two cases, namely, when
the perturation becomes of a linear operator and the case of non-linear
operator. We use the Lyapunov second method to guar- antee the global analysis
for the first case. For the second, we use the Hartman-Grobman theorem,
providing local analysis.

36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org