| 引用本文： |
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王琦,陈占和,张更容.一类高阶有理差分方程非负解的收敛性[J].广西科学,2013,20(2):88-90. [点击复制]
- WANG Qi,CHEN Zhan-he,ZHANG Geng-rong.Convergence of the Non-negative Solutions of a Higher-order Rational Difference Equation[J].Guangxi Sciences,2013,20(2):88-90. [点击复制]
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| 摘要: |
| 针对高阶有理差分方程xn+1=α+(∑i=1k+1 B2i-1xn-2i+1)/(A+xn-2l),n=0,1,…,其中k,l为非负整数,α是正数,A,Bi,i=1,2,…,k+1和初始条件是非负数,给出该方程的每个非负解都收敛于方程的一个二周期解的一个充分条件. |
| 关键词: 差分方程 收敛性 二周期解 有界性 |
| DOI： |
| 投稿时间：2013-02-16修订日期：2013-04-01 |
| 基金项目:This work was supported by NSF of China(No.11161029,No.11261005),NSF of Guangxi(No.2010GXSFA013109,No.2012GXSFA276040),NSF of Guangxi University of Technology(No.1166218)。 |
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| Convergence of the Non-negative Solutions of a Higher-order Rational Difference Equation |
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WANG Qi1, CHEN Zhan-he2, ZHANG Geng-rong2
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| (1.College of Science, Guangxi University of Science and Technology, Liuzhou, Guangxi, 545006, China;2.College of Mathematics and Information Sciences, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| This paper is concerned with the following higher-order rational difference equation:xn+1=α+(∑i=1k+1 B2i-1xn-2i+1)/(A+xn-2l),n=0,1,… where k and l are non-negative integers,the parameter α is positive real number,the parameters A,Bi,i=1,2,…,k+1 and the initial conditions are non-negative real numbers.We give the sufficient conditions, under which every non-negative solution of the equation converges to a period-two solution of the equation. |
| Key words: difference equation convergence period-two solution boundedness |
