LI Xiaoyan,XIE Jianmin.Global behavior of a higher-order rational difference equation[J].Journal of Yanbian University,2016,42(04):302-305.
一类高阶有理差分方程的全局行为
- Title:
- Global behavior of a higher-order rational difference equation
- Keywords:
- difference equation; equilibrium; stability; global attractor
- 分类号:
- O175
- 文献标志码:
- A
- 摘要:
- 考虑一类有理差分方程yn+1=A+(yn)/(ki=1yn-i), n=0,1,….首先利用判定稳定性的线性近似法和赫尔维茨判据、儒歇定理得到该方程正平衡点的局部性质; 然后证明了二阶有理差分方程的解的全局吸引性并推广到高阶有理差分方程的情形; 最后利用推广的结果得到当方程的系数满足一定条件时,该方程的唯一平衡点是一个全局吸引子.
- Abstract:
- In this article, the rational difference equation yn+1=A+(yn)/(ki=1yn-i)(n=0,1,…)is investigated. In terms of linear approximation, Rouché’s theorem and Hurwitz criterion, some sufficient conditions ensuring the local properties of positive equilibrium are derived. We proved the global attraction of second order rational difference equation. All the obtained results can be generalized to higher order difference equation. In addition, by employing the results of the generalization, we show that the unique positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient.
参考文献/References:
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备注/Memo
收稿日期: 2016-06-15 作者简介: 李晓艳(1980—),女,讲师,研究方向为运筹学与控制论.
基金项目: 国家自然科学地区科学基金资助项目(11661048); 2014陇原青年创新人才扶持计划项目