Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sincroniza\c{c}\~ao em Redes Complexas: Estabilidade e Persist\^encia   We investigate emergence of the global collective behavior in networks of
diffusively coupled identical oscillators, which in the established model is an
invariant manifold of the motion equations. The interaction is modeled with the
graph theory and dynamical systems theory. We use the uniform contractions
theory in non-autonomous linear differential equations to address the criterion
under the global coupling parameter, which it turns defines the synchronized
motion and it stability under small linear and non-linear perturbations. The
critical global interaction parameter is given only by the isolated dynamics,
by the spectral properties of the coupling function and the second eigenvalue
network laplacian.

5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th