线性差分方程的周期解  

Periodic solutions of linear difference equations

作　　者：王琦 尤卫玲 张更容[2] WANG Qi;YOU Weiling;ZHANG Gengrong(Public Course Teaching Department,Guangdong Open University,Guangzhou 510091,China;School of Mathematics and Statistics,Hunan First Normal University,Changsha 410205,China)

机构地区：[1]广东开放大学公共课教学部,广东广州510091 [2]湖南第一师范学院数学与统计学院,湖南长沙410205

出　　处：《安徽大学学报（自然科学版）》2023年第3期16-21,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11861013,11771149,12171113);湖南省自然科学基金资助项目(2018JJ2074);广西高校中青年教师基础能力提升项目(2018ky0327);广东开放大学人才专项科研项目(RC1926)。

摘　　要：研究一类高阶线性差分方程的周期解,给出一个充分必要条件,应用上极限、同余等相关理论知识,证明了方程的非负解都收敛于方程的一个d-周期解的结论.最后通过数值模拟,验证了结论的正确性,且结合已得到结论,发现线性差分方程展示出三分法特征,为研究一般差分方程的周期解提供了一种思路.In this paper,the periodic solution of a class of high-order linear difference equations is studied,a sufficient and necessary condition is given.By applying the relevant theoretical knowledge of superior limit and congruence,it is proved that the non-negative solution of the equation converges to a d-periodic solution of the equation.Finally,the correctness of our conclusion is verified by numerical simulation.Combined with the obtained results,we find that the linear difference equation shows the trichotomy character.This paper provides an idea for studying the periodic solution of the general difference equation.

关 键 词：线性差分方程 周期解 平衡点 同余 三分法特征 

分 类 号：O175[理学—数学] O241[理学—基础数学]