Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant cone and synchronization state stability of the mean field
  models   In this article we prove the stability of mean field systems as the Winfree
model in the synchronized state. The model is governed by the coupling strength
parameter $\kappa$ and the natural frequency of each oscillator. The stability
is proved independently of the number of os-cillators and the distribution of
the natural frequencies. In order to prove the main result, we introduce the
positive invariant cone and we start by studying the linearized system. The
method can be applied to others mean field models as the Kuramoto model.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat