文章基本信息

标题：Dynamic behavior of a nonlinear rational difference equation and generalization
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作者：Qihong Shi ; Qian Xiao ; Guoqiang Yuan 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2011
卷号：2011
期号：1
页码：36
DOI：10.1186/1687-1847-2011-36
语种：English
出版社：Hindawi Publishing Corporation
摘要：This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x n = (x n-k + x n-m + x n-l )/(x n-k x n-m + x n-m x n-l +1) with the initial data { x - l , x - l + 1 , … , x - 1 } ∈ ℝ + l and 1 ≤ k ≤ m ≤ l. The convergence of solution to this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et al. Appl. Math. Lett. 20:54-58, 2007; Papaschinopoulos and Schinas J Math Anal Appl 294:614-620, 2004) to a large extent. In addition, some propositions for generalized equations are reported.
关键词：Nonlinear; Difference equation ; Global stability ; Positive solution