Global asymptotic behavior and boundedness of positive solutions to an odd-order rational difference equation

被引：4
|
作者：
Liao, Maoxin [1 ,2 ]
Li, Xianyi [3 ]
Tang, Xianhua [1 ]
机构：
[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China
[2] Univ S China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China
[3] Shenzhen Univ, Sch Math & Computat Sci, Shenzhen 518060, Guangdong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2008年 / 56卷 / 02期
基金：
中国国家自然科学基金;
关键词：
odd-order rational difference equation; positive equilibrium point; global asymptotic stability; boundedness; transformation method;
D O I：
10.1016/j.camwa.2007.12.004
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note we consider the following high-order rational difference equation x(n) = 1 + Pi(k)(i =1)(1-x(n-i))/Sigma(k)(i=1)x(n-i), n = 0,1,..., where k >= 3 is odd number, x(-k), x(-k+1), x(k+2)(-),..., x(-1) is positive numbers. We obtain the boundedness of positive solutions for the above equation, and with the perturbation of initial values, we mainly use the transformation method to prove that the positive equilibrium point of this equation is globally asymptotically stable. (C) 2008 Elsevier Ltd. All rights reserved.
引用
收藏
页码：305 / 310
页数：6
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