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一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学

乐源

乐源. 一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学[J]. 力学学报, 2016, 48(1): 163-172. doi: 10.6052/0459-1879-15-144
引用本文: 乐源. 一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学[J]. 力学学报, 2016, 48(1): 163-172. doi: 10.6052/0459-1879-15-144
Yue Yuan. LOCAL DYNAMICAL BEHAVIOR OF TWO-PARAMETER FAMILY NEAR THE NEIMARK-SACKER-PITCHFORK BIFURCATION POINT IN A VIBRO-IMPACT SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 163-172. doi: 10.6052/0459-1879-15-144
Citation: Yue Yuan. LOCAL DYNAMICAL BEHAVIOR OF TWO-PARAMETER FAMILY NEAR THE NEIMARK-SACKER-PITCHFORK BIFURCATION POINT IN A VIBRO-IMPACT SYSTEM[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 163-172. doi: 10.6052/0459-1879-15-144

一类碰撞振动系统在内伊马克沙克-音叉分岔点附近的局部两参数动力学

doi: 10.6052/0459-1879-15-144
基金项目: 国家自然科学基金资助项目(11272268,11172246).
详细信息
    通讯作者:

    乐源,副教授,主要研究方向:动力系统的分岔与混沌、非光滑动力学.E-mail:yueyuan2011@home.swjtu.edu.cn

  • 中图分类号: O313

LOCAL DYNAMICAL BEHAVIOR OF TWO-PARAMETER FAMILY NEAR THE NEIMARK-SACKER-PITCHFORK BIFURCATION POINT IN A VIBRO-IMPACT SYSTEM

  • 摘要: 考虑一类具有对称性的三自由度碰撞振动系统. 系统的庞加莱映射在一定条件下存在对称不动点,对应于系统的对称周期运动. 根据对称性导出庞加莱映射 P 是另外一个隐式虚拟映射 Q 的二次迭代. 推导了庞加莱映射对称不动点的解析表达式. 根据映射不动点的稳定性及分岔理论,映射 P 的对称不动点发生内伊马克沙克- 音叉(Neimark-Saker-pitchfork) 分岔对应于映射 Q 发生内伊马克沙克- 倍化(Neimark-Sakerflip)分岔. 利用隐式虚拟映射 Q ,通过对范式作两参数开折分析,研究了映射 P 的对称不动点在内伊马克沙克-音叉分岔点附近的局部动力学行为. 碰撞振动系统在这个余维二分岔点附近的局部动力学行为可能表现为投影后的庞加莱截面上的单一对称不动点、一对共轭不动点、单一对称拟周期吸引子以及一对共轭拟周期吸引子. 数值模拟得到了内伊马克沙克-音叉分岔点附近的各种可能情况. 内伊马克沙克-分岔和音叉分岔互相作用可能产生新的结果:对称不动点虽然首先分岔为两个共轭不动点,但是这两个共轭不动点是不稳定的,最终收敛到同一个对称拟周期吸引子.

     

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出版历程
  • 收稿日期:  2015-04-23
  • 修回日期:  2015-07-14
  • 刊出日期:  2016-01-18

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