一类高阶非线性差分方程的吸引性  

The Attractivity of a Class of Higher Order Nonlinear Difference Equations

作　　者：葛琦[1] 张景琳[1] 

机构地区：[1]延边大学理学院数学系,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2010年第3期213-220,共8页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(10661011)

摘　　要：在文献[1-2]的基础上,研究了非线性差分方程xn+1=a-bxpn-k/A-x2n的全局稳定性和正解的周期性,其中a,A为非负实数,b为正实数,k,p∈{1,2,…},p≥2.证明了该方程的一个正平衡点是一个全局吸引子,并给出了相应的吸引域.On the basis of literature ,we study the global stability and the periodic character of the positive solution of the difference equations xn＋1=a-bxn-k^p/A-xn^2,where a,A are nonnegative real number,b is positive real number and k,p∈{1,2,…},p≥2.We show that the positive equilibrium of the equations is a global attractor with a basin that depends on certain conditions posed on the coefficients by analysis method.

关 键 词：差分方程 正平衡解 吸引性 

分 类 号：O175.8[理学—数学]