摘要
本文研究一个二维离散抛物映射的动力学行为.首先,引用文献[1]中关于映射不动点的存在性和稳定性的结果:映射有三个不动点,及当参数b变化时,每个不动点稳定性的充分条件;接着,把b作为分支参数,利用中心流形定理和分支理论,分别导出Fold分支、Flip分支、Hopf分支存在的充分条件;最后通过数值模拟,验证Fold分支、Flip分支、Hopf分支存在条件的理论结果,同时,也发现映射存在复杂的对称性破缺分支.
In this paper, the dynamical behaviors of a two-dimensional discrete parabolic map are investigated in detail. Firstly, the existence and stability of fixed point of the map are cited as presented in[3] that it has three fixed points and the sufficient conditions of their stability are obtained, respectively, when the parameter b changes. Secondly, sufficient conditions are derived for the existence of Fold bifurcation, Flip bifurcation and Hopf bifurcation by using the center manifold theorem and the bifurcation theory. Finally, using numerical simulation, we verify the existence of the Fold bifurcation, the Flip bifurcation and the Hopf bifurcation of the map. Meanwhile, the complex symmetry breaking bifurcation phenomenon of the map is observed.
作者
陈苏
袁少良
周慧
Cheng Su;Yuan Shaoliang;Zhou Hui(College of Mathematics and Computer Sciences, Yichun University, Yichun 336000, China)
出处
《动力学与控制学报》
2019年第2期97-103,共7页
Journal of Dynamics and Control
基金
江西省教育厅科学技术研究项目(GJJ170890)
国家自然科学基金资助项目(11361067)~~
