一类碰撞振动系统的余维二分叉和Hopf分叉*

本文研究弹簧质量系统对无穷大平面碰撞振动的分叉问题。证明了在接近完全弹性碰撞和在一些特殊的频率比附近,存在余维二分叉现象。利用映射的正则型理论,将Poincaré映射变换成含两个参数的正则型,通过分析该正则型,我们得到周期倍化分叉、周期1点、2点的Hopf分叉。并进行了数值验证。

Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System

In this paper,a spring-mass system impactillg against an infinite large plane is analyzed.We have proved that phenomenons of codimension two bifurcations exist when coefficient of restitution is near one and ratios of frequency near the same special values.method of normal forms, we reduced Poincare maps into normal forms containing two parameters.After studying these normal forms, we obtained period doublillg bifurcations and Hopf bifurcations of period-one and period-two.The results have been verifled by numerical works.