一类差分方程的动力学性质  

Dynamic Properties of a Class of Difference Equations

作　　者：李明山 徐江明 周效良 LI Mingshan;XU Jiangming;ZHOU Xiaoliang(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106;School of Mathematics and Statistics,Lingnan Normal University,Zhanjiang Guangdong 524048,China)

机构地区：[1]南京航空航天大学经济与管理学院,南京211106 [2]岭南师范学院数学与统计学院,广东湛江524048

出　　处：《重庆师范大学学报（自然科学版）》2021年第3期62-67,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11961021);广东省大学生科技创新培育专项资金(No.pdjh2021b0309);广东省高校重点项目(No.2019KZDXM032)。

摘　　要：【目的】研究一类差分方程的动力学性质。【方法】通过讨论系数参数与特征值的关系得到了双曲不动点的类型与稳定性,利用中心流形定理和分支理论研究了非双曲不动点的稳定性与flip分支,通过正规形理论与嵌入连续流等方法研究了特征值为±1的退化不动点的稳定性。【结果】得到了2-周期轨的稳定性、非双曲不动点的拓扑结构和退化不动点的稳定性。【结论】得到了一类差分方程的动力学性质。[Purposes]The dynamic properties of a class of difference equations are studied.[Methods]Firstly,the types and stability of hyperbolic fixed points are obtained by discussing the relationship between coefficient parameters and eigenvalues,and then the stability and flip bifurcation of non-hyperbolic fixed points are studied by using center manifold theorem and bifurcation theory.By means of normal form theory and embedded continuous flow method,the stability of the degenerate fixed point with eigenvalues±1 is obtained.[Findings]The stability of 2-periodic orbit,the topological structures of non-hyperbolic fixed points and the stability of the degenerate fixed point are given.[Conclusions]The dynamic properties of a class of difference equations are obtained.

关 键 词：差分方程 flip分支 中心流形定理 退化不动点 稳定性 

分 类 号：O175.7[理学—数学]