Symmetry,cusp bifurcation and chaos of an impact oscillator between two rigid sides

作     者：乐源 谢建华 

作者机构：Department of Applied Mechanics and Engineering Southwest Jiaotong UniversityChengdu 610031P.R.China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2007年第28卷第8期

页      面：1109-1117页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Project supported by the National Natural Science Foundation of China (No.10472096) the Fund for Doctoral Innovation of Southwest Jiaotong University 

主　　题：periodic motion Poincaémap symmetry pitchfork bifurcation chaotic attractor cusp 

摘      要：Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincar6 map. The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation. While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences, and bring about two antisymmetric chaotic attractors subse- quently. If the symmetric system is transformed into asymmetric one, bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.