关于一类非线性差分方程的解的频率收敛分析  

Frequent convergence for solutions of a class of nonlinear difference equation

作　　者：卜繁强[1] 李慧[2] 陶元红[2] 

机构地区：[1]延边大学师范分院,延吉133002 [2]延边大学理学院,延吉133002

出　　处：《黑龙江大学自然科学学报》2015年第4期468-474,共7页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11361065);吉林省自然科学基金资助项目(201215239)

摘　　要：利用数列的频率测度定义及其性质,研究一类差分方程x2n+1=m-x n在3<m<1时的解4的频率收敛性。定义与所讨论差分方程密切相关的多项式函数,求出此函数的不动点,利用此函数在不同区间上的单调性,证明初始值取在区间[-1-4m-3(1/2)/2,1-1+4m(1/2)/2)∪(1-1+4m(1/2)/2,-1+4m-3(1/2)/2][1-4m-3(1/2)/2,-1+4m(1/2)/2)∪(-1+1+4m(1/2)/2,1+4m-3(1/2)/2]中时,差分方程的解有两个0.5度频率极限1+4m-3(1/2)/2和1-4m-3(1/2)/2。Frequently convergence for solutions of a class of difference equation x n ＋ 1= m- x^2 nare dis-3cussed where m 1 by using definition and properties of frequency measure of real valued se-4quences. First of all,a polynomial function closely related to the difference equation is defined,and then its fixed points are presented. Finally,using monotone properties of this function in different interval,it[- 1- 4mis proved that if the initial values are in the interval [-1-√4m-3/2,1-√1＋4m/2）∪（1-√1＋4m/2,-1＋√4m-3/2][1-√4m-3/2,-1＋4m/2）∪（-1＋√1＋4m/2,1＋4m,-1＋√4m-3/2],then the solutions of the difference equation have two frequent limits 1＋√4m-3/2 and 1-√4m-3/2 of degree 0. 5.

关 键 词：频率测度 频率收敛 频率属于 

分 类 号：O177.3[理学—数学]