| 差分方程yn+1=A+yn/(kΣi=1αiyn-i)的全局吸引性 |
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| 引用本文： | 胡正高,曾晓云,张德存. 差分方程yn+1=A+yn/(kΣi=1αiyn-i)的全局吸引性[J]. 海军航空工程学院学报, 2011, 26(1): 117-120 |
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| 作者姓名： | 胡正高 曾晓云 张德存 |
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| 作者单位： | [1]海军航空工程学院研究生管理大队,山东烟台264001 [2]海军航空工程学院基础部,山东烟台264001 |
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| 摘 要： | 研究差分方程yn+1=A+yn/(kΣi=1αiyn-i),N=0,1,...正解的稳定性,其中,A∈(0,∞),αi∈(0,∞),kΣi=1αi=k,k≥1且是整数,初始条件y-k,...,y0为任意正数.阐述并证明该方程的惟一正平衡点是全局吸引子且吸引域取决于方程的系数.
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| 关 键 词： | 差分方程 不变区间 稳定性 吸引性 |
Global Attractiveness of the Difference Equation |
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| HU Zheng-gao,ZENG Xiao-yun and ZHANG De-cun. Global Attractiveness of the Difference Equation[J]. Journal of Naval Aeronautical Engineering Institute, 2011, 26(1): 117-120 |
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| Authors: | HU Zheng-gao ZENG Xiao-yun ZHANG De-cun |
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| Affiliation: | (Naval Aeronautical and Astronautical University a. Graduate Students＇ Brigade; b. Department of Basic Sciences, Yantai Shandong 264001, China) |
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| Abstract: | In this paper, the global stability of all positive solutions of the difference equation yn＋1=A＋yn/（∑k i=1 ai yn-i） ,n=0,1,…
was studied, where A∈（0,∞）,ai∈（0,∞）,∑k i=1 ai=k,k≥1 is an integer, and the initial conditions y-k,…,y0 are arbitrary positive real numbers. It was showed that the unique positive equilibrium of the equation was a global attractor with a basin that depended on certain conditions of the coefficient. |
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| Keywords: | difference equation invariant intervals stability attractiveness |
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