一类有理差分方程动力学定理的证明  

Proof of dynamic theorems for a class of rational difference equations

作　　者：全卫贞 李晓培 凌伟钟 阿的史古 陈月婷 全国标 QUAN Weizhen;LI Xiaopei;LING Weizhong;ADI Shigu;CHEN Yueting;QUAN Guobiao(Department of Mathematics,Zhanjiang Preschool Education College,Zhanjiang 524084,China;Basic Education College,Lingnan Normal University,Zhanjiang 524037,China)

机构地区：[1]湛江幼儿师范专科学校数学系,广东湛江524084 [2]岭南师范学院基础教育学院,广东湛江524037

出　　处：《苏州科技大学学报（自然科学版）》2023年第2期27-30,50,共5页Journal of Suzhou University of Science and Technology（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11761011);广东省普通高校特色创新项目(2020KTSCX351);广东省“攀登计划”重点项目(PDJH2020A1315)。

摘　　要：为了让相关研究者能够深入掌握Kulenovic等给出的有理差分方程x_(n+1)=(px_(n)+x_(n-1))/(q+x_(n-1))的动力学定理,论文根据二阶有理差分方程的理论,采用3种方法证明了该动力学定理,也就是通过改变不同的条件,得到了平衡解■的局部渐近稳定性、全局渐近稳定性、排斥点或不稳定鞍点等结论。In order to deeply grasp the dynamic theorems of rational difference equations x_(n+1)=(px_(n)+x_(n-1))/(q+x_(n-1))given by kulenovic,this paper proved the dynamic theorems by three methods,based on the theories of second order rational difference equations.By setting different conditions,we obtained different results such as locally asymptotical stability,globally asymptotical stability,repelling points or unstable saddle points of the equilibrium solution■.

关 键 词：差分方程 平衡解 局部渐近稳定 不稳定鞍点 排斥点 

分 类 号：O175.7[理学—数学]