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.
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)
出处
《重庆师范大学学报（自然科学版）》
CAS
北大核心
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)。
关键词
差分方程
flip分支
中心流形定理
退化不动点
稳定性
difference equation
flip bifurcation
center manifold theorem
degenerated fixed point
stability
