摘要
研究一类多滞量偏差分方程xm+1,n+axm,n+1=1+(xm-k,n-blxm-2k,n-2l)p,m,n=0,1,2,…,其中:i)a,b∈(0,+∞),k,l,p∈N+={1,2,…};ii){xm,n}满足初始条件:xm,n=m,n>0,对每个(m,n)∈Ω0,Ω0={(m,n)|m≥-2k,n≥-2l}\{(m,n)|m≥1,n≥0}.首先建立了其解的持久性和振动性的充分条件,并将方程的解与引理2中的收敛数列进行比较,利用数学归纳法证明了解的一致渐近稳定性。
Consider partial difference equation
xm＋1,a＋axm,n＋1=b/1＋（xm-k,n-lxm-2k,n-21）^p,m,n=0,1,2…,where：i）1,b∈（0,＋∞）,k,l,P∈n^＋={1,2,…｜;ii）｜xm,n｜satisfies xm,n=Φm,n〉0,for all（m,n）∈Ω0,Ω0=（m,n）｜m≥-2k,n∈-2l｜／｜（m,n）｜m≥1,n≥0｜.
Firstly, the sufficient conditions of the permanence and oscillation of the solutions are established. Next, the solutions of the partial difference equation are compared with the convergent sequences of lemma 2. By means of mathematical induction method, unform asymptotic stability of the solutions of the partial difference equation is obtained.
出处
《黑龙江大学自然科学学报》
CAS
北大核心
2008年第1期29-33,41,共6页
Journal of Natural Science of Heilongjiang University
基金
国家自然科学基金资助项目(10661011)
关键词
偏差分方程
持久性
振动性
吸引性
渐近稳定性
partial difference equation
permanence
oscillation
attractor
asymptotic stability
