一类高阶有理差分方程的动力学性质  

Dynamic properties of a class of higher order rational difference equations

作　　者：全卫贞 李晓培 黄日娣 王丽 周敬人 刘付滢 江建伟 刘世祺 QUAN Weizhen;LI Xiaopei;HUANG Ridi;WANG Li;ZHOU Jingren;LIU Fuying;JIANG Jianwei;LIU Shiqi(Department of Mathematic,Zhanjiang Preschool Education College,Zhanjiang 524037,China;School of Basic Education,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524037 [2]岭南师范学院基础教育学院,广东湛江524037

出　　处：《高师理科学刊》2023年第7期1-5,共5页Journal of Science of Teachers＇College and 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：应用高阶有理差分方程的知识理论,给出了高阶有理差分方程x_(n+1)p+qx_(n-1)/1+x_(n-t)+rx_(n-s)的若干个动力学定理,得到了解的有界性和正平衡解的局部渐近稳定性、全局渐近稳定性和素二周期解等结论,并用Matlab的数值计算来印证结论.By using the knowledge theory of higher order rational difference equations,several dynamic theorems of higher order rational difference equation x_(n+1)p+qx_(n-1)/1+x_(n-t)+rx_(n-s)were given,the boundedness of solutions,local asymptotic stability,global asymptotic stability,prime two periodic solutions of positive equilibrium solutions was obtained,and finally Matlab′s numerical calculations was used to confirm the conclusions.

关 键 词：差分方程 平衡解 局部渐近稳定 全局渐近稳定 素二周期解 

分 类 号：O175.7[理学—数学]