On some systems of difference equations

被引：127

作者：

Berg, Lothar ^{[2
]}

Stevic, Stevo ^{[1
]}

机构：

[1] Serbian Acad Sci, Math Inst, Beograd 11000, Serbia

[2] Univ Rostock, Inst Math, D-18051 Rostock, Germany

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 218卷 / 05期

关键词：

System of difference equations; Riccati equations; Asymptotics; Periodicity; Convergence; Boundedness; Symmetric systems; GLOBAL STABILITY; HIGHER-ORDER; NONTRIVIAL SOLUTIONS; ASYMPTOTICS; XN+1;

D O I：

10.1016/j.amc.2011.06.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we show that the following systems of difference equations u(n+1) = v/1+v(n), v(n+1) = u(n)/1+u(n), u(n+1) = v(n)/1+u(n), v(n+1) = u(n)/1+v(n), u(n+1) = u(n)/1+v(n), v(n+1) = v(n)/1+u(n) with n is an element of N-0 and complex initial values u(0) and v(0), are solvable explicitly by means of Riccati equations, and based on the formulae for the general solutions we present the behaviour of their solutions as n -> infinity. While the result is natural for the first system, it is a bit surprising for the other two systems. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1713 / 1718

页数：6

共 25 条

[1]

Berg L, 2002, Z ANAL ANWEND, V21, P1061

[2] On the asymptotics of the difference equation [J].