zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Asymptotic behavior of equilibrium point for a family of rational difference equations. (English) Zbl 1204.39011
Summary: This paper is concerned with the following nonlinear difference equation $$x_{n+1}=\sum_{i=1}^l A_{s_i}x_{n-s_i}/(B+C\prod_{j=1}^k x_{n-t_j})+Dx_n,\quad n=0,1,\ldots,$$ where the initial data $x_{-m},x_{-m+1},\ldots,x_{-1},x_0\in\Bbb{R}^+$, $m=\max\{s_1,\ldots,s_l,t_1,\ldots,t_k\}$, $s_1,\ldots,s_l$, $t_1,\ldots,t_k$ are nonnegative integers, and $A_{s_i}, B, C$ and $D$ are arbitrary positive real numbers. We give sufficient conditions under which the unique equilibrium $\Bar{x}=0$ of this equation is globally asymptotically stable, which extends and includes corresponding results obtained in the work of {\it C. Çinar} [Appl. Math. Comput. 150, No. 1, 21--24 (2004; Zbl 1050.39005)], {\it X. Yang} et al. [Appl. Math. Comput. 162, No. 3, 1485--1497 (2005; Zbl 1068.39031)], and {\it K. S. Berenhaut} et al. [Appl. Math. Lett. 20, No. 1, 54--58 (2007; Zbl 1131.39006)]. In addition, some numerical simulations are also shown to support our analytic results.

39A22Growth, boundedness, comparison of solutions (difference equations)
Full Text: DOI EuDML