Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian integrals and limit cycles for a class of cubic polynomial
  vector fields of Lotka-Volterra type with a rational first integral of degree
  2   In this paper, we study the number of limit cycles which bifurcate from the
periodic orbits of cubic polynomial vector fields of Lotka-Volterra type having
a rational first integral of degree 2, under polynomial perturbations of degree
$n$. The analysis is carried out by estimating the number of zeros of the
corresponding Abelian integrals. Moreover, using \emph{Chebyshev criterion}, we
show that the sharp upper bound for the number of zeros of the Abelian
integrals defined on each period annulus is 3 for $n=3$. The simultaneous
bifurcation and distribution of limit cycles for the system with two period
annuli under cubic polynomial perturbations are considered. All configurations
$(u,v)$ with $0\leq u, v\leq 3, u+v\leq5$ are realizable.

22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex