Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proving the existence of numerically detected planar limit cycles   This paper deals with the problem of location and existence of limit cycles
for real planar polynomial differential systems. We provide a method to
construct Poincar\'e--Bendixson regions by using transversal curves, that
enables us to prove the existence of a limit cycle that has been numerically
detected. We apply our results to several known systems, like the Brusselator
one or some Li\'{e}nard systems, to prove the existence of the limit cycles and
to locate them very precisely in the phase space. Our method, combined with
some other classical tools can be applied to obtain sharp bounds for the
bifurcation values of a saddle-node bifurcation of limit cycles, as we do for
the Rychkov system.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics