| 一类高阶有理差分方程的全局渐近稳定性 |
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| 引用本文： | 张永玲.一类高阶有理差分方程的全局渐近稳定性[J].云南民族大学学报(自然科学版),2015,24(1):37-42. |
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| 作者姓名： | 张永玲 |
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| 作者单位： | 兰州交通大学数理学院,甘肃兰州,730070 |
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| 基金项目： | 国家自然科学基金，国家自然基金甘肃省级联合基金，陇原青年创新人才支持计划，兰州交通大学青年基金 |
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| 摘 要： | 研究差分方程xn+1=xn+αxn-k/Axn+Bxn-k,n=0,1,2,…,所有正解的局部稳定性、素二周期解、有界性、不变区间和全局渐近稳定性,其中α,A,B∈(0,∞),k∈{1,2,3,…},初始条件x-k,…,x0是任意的正整数.获得了此方程的唯一正平衡点是全局渐近稳定的.
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| 关 键 词： | 正平衡点 不变区间 全局吸引子 全局渐近稳定 |
The global asymptotic stability of a higher-order difference equation |
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| ZHANG Yong-ling.The global asymptotic stability of a higher-order difference equation[J].Journal of Yunnan Nationalities University:Natural Sciences Edition,2015,24(1):37-42. |
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| Authors: | ZHANG Yong-ling |
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| Institution: | ,School of Mathematics and Physics,Lanzhou Jiaotong University |
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| Abstract: | This paper investigates the local stability,prime period-two solutions,boundedness,invariant intervals,and the global asymptotic stability of all positive solutions of the following difference equation xn+1=xn+ αxn-k/Axn+Bxn-k,n=0,1,2,…,where α,A,B∈(0,∞),k∈{1,2,3,…},and the initial conditions x-k,…,x(0∈0,∞).It concludes that the unique equilibrium of the equation is globally asymptotically stable under certain conditions. |
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| Keywords: | positive equilibrium point invariant intervals global attractor global asymptotic stability |
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