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余维三fold-fold-Hopf分岔下簇发振荡及其分类

薛淼 葛亚威 张正娣 毕勤胜

薛淼, 葛亚威, 张正娣, 毕勤胜. 余维三fold-fold-Hopf分岔下簇发振荡及其分类[J]. 力学学报, 2021, 53(5): 1423-1438. doi: 10.6052/0459-1879-21-024
引用本文: 薛淼, 葛亚威, 张正娣, 毕勤胜. 余维三fold-fold-Hopf分岔下簇发振荡及其分类[J]. 力学学报, 2021, 53(5): 1423-1438. doi: 10.6052/0459-1879-21-024
Xue Miao, Ge Yawei, Zhang Zhengdi, Bi Qinsheng. BURSTING OSCILLATIONS AS WELL AS THE CLASSIFICATION IN THE FIELD WITH CODIMENSION-3 FOLD-FOLD-HOPF BIFURCATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1423-1438. doi: 10.6052/0459-1879-21-024
Citation: Xue Miao, Ge Yawei, Zhang Zhengdi, Bi Qinsheng. BURSTING OSCILLATIONS AS WELL AS THE CLASSIFICATION IN THE FIELD WITH CODIMENSION-3 FOLD-FOLD-HOPF BIFURCATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1423-1438. doi: 10.6052/0459-1879-21-024

余维三fold-fold-Hopf分岔下簇发振荡及其分类

doi: 10.6052/0459-1879-21-024
基金项目: 1)国家自然科学基金资助项目(116232008)
详细信息
    作者简介:

    2)毕勤胜, 教授, 主要研究方向: 非线性动力学. E-mail: qbi@ujs.edu.cn

    通讯作者:

    薛淼

  • 中图分类号: O322

BURSTING OSCILLATIONS AS WELL AS THE CLASSIFICATION IN THE FIELD WITH CODIMENSION-3 FOLD-FOLD-HOPF BIFURCATION

  • 摘要: 不同尺度耦合系统存在着广泛的工程背景, 通常表现为大幅振荡与微幅振荡交替出现的簇发振荡, 其产生机理一直是当前国内外研究的前沿课题之一. 传统的几何奇异摄动分析方法仅对时域上的两尺度耦合有效, 无法揭示频域上不同尺度之间的相互作用, 同时, 当前相关研究仅针对余维一fold或Hopf分岔展开. 本文针对频域两尺度耦合向量场存在余维三fold-fold-Hopf分岔时的复杂动力特性, 基于包含三阶非线性项以内的该分岔向量场的标准型及其普适开折, 给出相应的分岔集, 从而将双开折参数平面划分为对应于不同行为的子区域. 引入慢变周期激励项取代其中一个开折参数, 随慢变激励项的变化, 会存在两类轨迹访问子区域途径, 产生周期Hopf/LPC, Hopf/LPC/Hopf/LPC, fold/LPC/Hopf/Homoclinic和fold/LPC 4种簇发振荡类型. 在分析过程中, 发现系统轨迹上的真实分岔, 往往与理论上的分岔点之间存在着滞后效应, 这种滞后效应的滞后时间也会随着激励幅值的增大而延长, 因为激励幅值的增大, 会导致轨迹沿相应平衡态运动的惯性增大, 特别是, 当激励幅值增大到一定值后, 会导致轨迹沿某平衡态运动并穿越该区域, 也即相关分岔效应来不及出现, 从而导致振荡形式的改变. 本工作表明, 对于局部分岔下的快慢效应, 通过向量场标准型开折参数的周期扰动, 在一定程度可以对该分岔所导致的所有可能的各种簇发进行归类, 并得到其相应的产生机制.

     

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出版历程
  • 收稿日期:  2020-01-15
  • 刊出日期:  2021-05-18

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