双边碰撞Duffing振子的对称性、尖点分岔与混沌
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西南交通大学 力学与工程学院,成都 610031

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E-mail: gql6321@163.comE-mail:gql6321@163.com

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国家自然科学基金资助重点项目(11732014)


SYMMETRY, CUSP BIFURCATION AND CHAOS OF THE DOUBLE-IMPACT DUFFING OSCILLATOR
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School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China

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The key project supported by the National Natural Science Foundation of China(11732041)

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    摘要:

    以单自由度双边碰撞Duffing振子的对称系统以及非对称系统为研究对象.分析了对称系统Poincaré映射的对称性,借助不连续映射和打靶法分析系统的周期解及稳定性.数值模拟表明:对于对称系统,首先一条对称周期轨道通过音叉分岔形成两条具有相同稳定性的反对称周期轨道,然后两条反对称的周期轨道分别经历两个同步的周期倍化分岔各自生成一个反对称的混沌吸引子,最后两个反对称的混沌吸引子融合为同一个对称的混沌吸引子.对于非对称系统,非对称周期运动的分岔可用一个两参数开折的尖点分岔描述,音叉分岔过程发生了典型的对称破缺现象.

    Abstract:

    Both symmetric and asymmetric systems of one-degree-of-freedom double-impact Duffing oscillators are considered. The symmetry of Poincaré mapping is analyzed. By means of discontinuous mapping and the shooting method, periodic solution and its stability of the system are analyzed. Numerical simulation indicates that for the symmetric system, firstly a symmetric periodic orbit bifurcates into two antisymmetric period orbits, being of same stability, and the two antisymmetric periodic orbits go through two synchronous period-doubling bifurcations to form two antisymmetric chaotic attractors subsequently. Finally, the two antisymmetric chaotic attractors are fused into one symmetric chaotic attractor. For the asymmetric system, an asymmetric periodic motion can be characterized by a two-parameter unfolding of cusp bifurcation, and a typical symmetric breaking phenomenon takes place during pitchfork bifurcation.

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李冠强,谢建华.双边碰撞Duffing振子的对称性、尖点分岔与混沌[J].动力学与控制学报,2021,19(5):1~7; Li Guanqiang, Xie Jianhua. SYMMETRY, CUSP BIFURCATION AND CHAOS OF THE DOUBLE-IMPACT DUFFING OSCILLATOR[J]. Journal of Dynamics and Control,2021,19(5):1-7.

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历史
  • 收稿日期:2020-06-23
  • 最后修改日期:2020-08-31
  • 录用日期:2020-09-13
  • 在线发布日期: 2021-11-08
  • 出版日期: 2021-10-15

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