Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Synchronization on Connected Undirected Networks   This paper gives sufficient conditions for having complete synchronization of
oscillators in connected undirected networks. The considered oscillators are
not necessarily identical and the synchronization terms can be nonlinear. An
important problem about oscillators networks is to determine conditions for
having complete synchronization that is the stability of the synchronous state.
The synchronization study requires to take into account the graph topology. In
this paper, we extend some results to non linear cases and we give an existence
condition of trajectories. Sufficient conditions given in this paper are based
on the study of a Lyapunov function and the use of a pseudometric which enables
us to link network dynamics and graph theory. Applications of these results are
presented.

35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph