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双频激励下Filippov系统的非光滑簇发振荡机理

曲子芳 张正娣 彭淼 毕勤胜

曲子芳, 张正娣, 彭淼, 毕勤胜. 双频激励下Filippov系统的非光滑簇发振荡机理[J]. 力学学报, 2018, 50(5): 1145-1155. doi: 10.6052/0459-1879-18-136
引用本文: 曲子芳, 张正娣, 彭淼, 毕勤胜. 双频激励下Filippov系统的非光滑簇发振荡机理[J]. 力学学报, 2018, 50(5): 1145-1155. doi: 10.6052/0459-1879-18-136
Qu Zifang, Zhang Zhengdi, Peng Miao, Bi Qinsheng. NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1145-1155. doi: 10.6052/0459-1879-18-136
Citation: Qu Zifang, Zhang Zhengdi, Peng Miao, Bi Qinsheng. NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1145-1155. doi: 10.6052/0459-1879-18-136

双频激励下Filippov系统的非光滑簇发振荡机理

doi: 10.6052/0459-1879-18-136
基金项目: 1) 国家自然科学基金项目(11632008) , 国家自然科学基金项目(11472116) 和江苏省研究生科研与实践创新计划项目(KYCX17_1784) 资助.
详细信息
    作者简介:

    2) 张正娣, 教授, 主要研究方向: 动力学与控制. E-mail: dyzhang@ujs.edu.cn

    通讯作者:

    张正娣

  • 中图分类号: O322;

NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS

  • 摘要: 旨在揭示含双频周期激励的不同尺度Filippov系统的非光滑簇发振荡模式及分岔机制. 以Duffing和Van der Pol耦合振子作为动力系统模型,引入周期变化的双频激励项,当两激励频率与固有频率存在量级差时,将两周期激励项表示为可以作为一慢变参数的单一周期激励项的代数表达式,给出了当保持外部激励频率不变,改变参数激励频率的情况下,快子系统随慢变参数变化的平衡曲线及因系统出现的fold分岔或Hopf分岔导致的系统分岔行为的演化机制.结合转换相图和由Hopf分岔产生稳定极限环的演化过程,得到了由慢变参数确定的同宿分岔、多滑分岔的临界情形及因慢变参数改变而出现的混合振荡模式,并详细阐述了系统的簇发振荡机制和非光滑动力学行为特性.通过对比两种不同情形下的平衡曲线及分岔图,指出虽然系统有相似的平衡曲线结构, 却因参数激励频率取值的不同,致使平衡曲线发生了更多的曲折,对应的极值点的个数也有所改变,并通过数值模拟, 对结果进行了验证.

     

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出版历程
  • 收稿日期:  2018-04-25
  • 刊出日期:  2018-09-18

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