一类有理差分方程动力学性质的证明  

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;A Dishigu;CHEN Yueting;QUAN Guobiao(Department of Mathematics,Zhanjiang Preschool Education College;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 [2]岭南师范学院基础教育学院,广东湛江524037

出　　处：《玉溪师范学院学报》2022年第6期1-6,共6页Journal of Yuxi Normal 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动力学理论知识,采用不同的方法证明有理差分方程x_(n+1)=p+qx_(n-1)/1+x_(n)+rx_(n-1)的动力学性质,得到了正平衡解xˉ的局部渐近稳定性、全局渐近稳定性、不稳定性、或不稳定鞍点等不同的稳定性,最后给出存在素二周期解的条件.To deepen researchers’understanding of the dynamic theorems of rational difference equations given by kulenovic[1],x_(n+1)=p+qx_(n-1)/1+x_(n)+rx_(n-1),this paper proves the stability properties with different methods on the basis of the theories of second-order rational difference equation.By setting different conditions,we obtain different results such as local asymptotic stability,global asymptotic stability,instability,or unstable saddle point of the positive equilibrium solution.Finally,we give the conditions for the existence of prime two periodic solutions.

关 键 词：差分方程 平衡解 局部渐近稳定 全局渐近稳定 鞍点 素二周期解 

分 类 号：O175.7[理学—数学]