一类二阶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 Wei-zhen;LI Xiao-pei;LING Wei-zhong;ADI Shi-gu;CHEN Yue-ting;QUAN Guo-biao(Department of Mathematics, Zhanjiang Preschool Education College, Zhanjiang Guangdong 524037, China;School of Basic Education, Lingnan Normal 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,广东湛江524037

出　　处：《菏泽学院学报》2022年第2期1-5,共5页Journal of Heze University

基　　金：国家自然科学基金项目(11761011);广东省普通高校特色创新项目(2020KTSCX351)。

摘　　要：根据二阶有理差分方程的理论,采用3种方法证明了二阶有理差分方程xn+1=pxn+xn-1/r+qxn+xn-1的动力学定理,即通过设置不同的条件,得到了平衡解的局部渐近稳定性、不稳定性、排斥点或不稳定鞍点等不同的结果.According to the theory of second-order rational difference equation,three methods are used to prove the dynamic theorem of second-order rational difference equation xn+1=pxn+xn-1/r+qxn+xn-1,that is,by setting different conditions,different results such as local asymptotic stability,instability,repulsion point or unstable saddle point of the equilibrium solution are obtained.

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]