摘要
研究差分方程yn＋1=A＋yn/（∑k i=1 ai yn-i）,n=0,1，…正解的稳定性，其中，A∈（0,∞）,ai∈（0,∞）,∑k i=1 ai=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。
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.
出处
《海军航空工程学院学报》
2011年第1期117-119,共3页
Journal of Naval Aeronautical and Astronautical University
关键词
差分方程
不变区间
稳定性
吸引性
difference equation
invariant intervals
stability
attractiveness
