一类二阶有理差分方程的解的性质  

Asymptotic Behavior of Solutions for a Class of a Two-order Rational Difference Equation

作　　者：黄日娣 全卫贞 周敬人 王丽 HUANG Ridi;QUAN Weizhen;ZHOU Jingren;WANG Li(Department of Mathematic,Zhanjiang Preschool Education College,Guangdong 524037,China;Basic Education College,Lingnan Nor-mal University,Zhanjiang,Guangdong 524037,China)

机构地区：[1]湛江幼儿师范专科学校数学系,广东湛江524037 [2]岭南师范学院基础教育学院数学系,广东湛江524037

出　　处：《宜宾学院学报》2022年第12期89-92,共4页Journal of Yibin University

基　　金：国家自然科学基金项目(11761011);广东省“攀登计划”重点项目(pdjh2020a1315);广东省普通高校特色创新项目(2020KTSCX351);湛江市非资助科技攻关计划项目(2022B01198)。

摘　　要：用差分方程的动力学定理、Schur-Cohn和Routh-Hurwitz判别法两种方法研究二阶有理差分方程x_(n+1)=ax_(n)+x_(n-1)^(2)/bx_(n)+cx_(n-1)+d(其中a,b,c,d∈R^(+),x_(-1),x_(0)∈R^(+),n=0,1,2,…)的解{x_(n)}_(n=-1)^(∞)的渐近性.并由a,b,c,d的取值的不同,得到不同的解的渐近性,同时给出了平衡解是鞍点、汇点、排斥点、非双曲点的充要条件.The asymptotic behavior of the solution of the second-order rational difference equation x_(n+1)=ax_(n)+x_(n-1)^(2)/bx_(n)+cx_(n-1)+d(a,b,c,d∈R^(+),x_(-1),x_(0)∈R^(+),n=0,1,2,…)was studied by two different methods:the dynamic theorem of the difference equation,the Schur Cohn and Routh Hurwitz discriminant method.From the different values of a,b,c,d,the asymptotic properties of different solutions are obtained,and the necessary and sufficient conditions for the equilibrium solution to be a saddle point,a sink point,an exclusion point,and a non-hyperbolic point are given.

关 键 词：有理差分方程 动力学定理 Schur-Cohn和Routh-Hurwitz判别法 渐近性 

分 类 号：O175.12[理学—数学]