Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Behavior of Solutions to Two Classes of Second Order Rational
  Difference Equations   For nonnegative real numbers $\alpha$, $\beta$, $\gamma$, $A$, $B$ and $C$
such that $B+C>0$ and $\alpha+\beta+\gamma >0$, the difference equation
  \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma
x_{n-1}}{A+B x_{n}+C x_{n-1}}, \quad n=0,1,2,... %, \quad x_{-1},x_{0}\in
[0,\infty) \end{equation*} has a unique positive equilibrium. A proof is given
here for the following statements: \medskip
  \noindent Theorem 1. {\it For every choice of positive parameters $\alpha$,
$\beta$, $\gamma$, $A$, $B$ and $C$, all solutions to the difference equation
  \begin{equation*} x_{n+1}=\displaystyle\frac{\alpha +\beta x_{n}+\gamma
x_{n-1}}{A+B x_{n}+C x_{n-1}}, \quad n=0,1,2,..., \quad x_{-1},x_{0}\in
[0,\infty) \end{equation*} converge to the positive equilibrium or to a prime
period-two solution.} \medskip
  \noindent Theorem 2. {\it For every choice of positive parameters $\alpha$,
$\beta$, $\gamma$, $A$, $B$ and $C$, all solutions to the difference equation
\begin{equation*} x_{n+1}= \displaystyle\frac{\alpha +\beta x_{n}+\gamma
x_{n-1}}{B x_{n}+C x_{n-1}}, \quad n=0,1,2,..., \quad x_{-1},x_{0}\in
(0,\infty) \end{equation*} converge to the positive equilibrium or to a prime
period-two solution.}

10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg