Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global stability for the 2-dimensional logistic map   For the delayed logistic equation $x_{n+1} = a x_n (a-x_{n-1})$ it is well
known that the nontrivial fixed point is locally stable for $1<a\leq 2$, and
unstable for $a>2$. We prove that for $1<a\leq 2$ the fixed point is globally
stable, in the sense that it is locally stable and attracts all points of $S$,
where $S$ contains those $(x_0,x_1)\in \mathbb{R}_+^2$, for which the sequence
$\left\lbrace x_n\right\rbrace \subset \mathbb{R}_+$. The proof is a
combination of analytical and reliable numerical methods.

29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph