文章基本信息
- 标题：Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations
- 本地全文：下载
- 作者：Sukanya Basu ; Orlando Merino
- 期刊名称：Advances in Difference Equations
- 印刷版ISSN：1687-1839
- 电子版ISSN：1687-1847
- 出版年度：2009
- 卷号：2009
- DOI：10.1155/2009/128602
- 出版社：Hindawi Publishing Corporation
- 摘要：
For nonnegative real numbers α , β , γ , A , B , and C such that B + C > 0 and α + β + γ > 0 , the difference equation x n + 1 = ( α + β x n + γ x n − 1 ) / ( A + B x n + C x n − 1 ) , n = 0 , 1 , 2 , … has a unique positive equilibrium. A proof is given here for the following statements: (1) For every choice of positive parameters α , β , γ , A , B , and C , all solutions to the difference equation x n + 1 = ( α + β x n + γ x n − 1 ) / ( A + B x n + C x n − 1 ) , n = 0 , 1 , 2 , … , x − 1 , x 0 ∈ [ 0 , ∞ ) converge to the positive equilibrium or to a prime period-two solution . (2) For every choice of positive parameters α , β , γ , B , and C , all solutions to the difference equation x n + 1 = ( α + β x n + γ x n − 1 ) / ( B x n + C x n − 1 ) , n = 0 , 1 , 2 , … , x − 1 , x 0 ∈ ( 0 , ∞ ) converge to the positive equilibrium or to a prime period-two solution .
