摘要
应用中心流形范式方法研究了高维映射方程在非共振和弱共振情况下的 Ｈｏｐｆ 分叉问题，计算了中心流形，给出了映射的降维过程和简化方程，将 Ｒ２ 映射的 Ｈｏｐｆ分叉理论推广到了高维映射。应用该方法分析了一类两自由度冲击振动系统周期运动 Ｈｏｐｆ 分叉的存在性。
The Hopf bifurcation of high dimensional maps in non resonance and weak resonance cases are investigated by using the center manifold normal from method. The centre manifold is calculated and the steps for reduction of a high dimensional map to a two dimensional one are given. Then the theory of Hopf bifurcation of maps in R 2 is applied to high dimensional map. The Hopf bifurcations of a two degree freedom vibro impact system in non resonance and weak resonance cases are analyzed by means of the method. The theoretical analyses are well supported by numerical results, and the routes of quasi periodic impacts to chaos are obtained.
出处
《振动工程学报》
EI
CSCD
1999年第3期360-366,共7页
Journal of Vibration Engineering
基金
国家自然科学基金
甘肃省自然科学基金
