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Duffing系统在双参数平面上的分岔演化过程

张艳龙 王丽 石建飞

张艳龙, 王丽, 石建飞. Duffing系统在双参数平面上的分岔演化过程[J]. 应用数学和力学, 2018, 39(3): 324-333. doi: 10.21656/1000-0887.380089
引用本文: 张艳龙, 王丽, 石建飞. Duffing系统在双参数平面上的分岔演化过程[J]. 应用数学和力学, 2018, 39(3): 324-333. doi: 10.21656/1000-0887.380089
ZHANG Yanlong, WANG Li, SHI Jianfei. Bifurcation Evolution of Duffing Systems on 2-Parameter Planes[J]. Applied Mathematics and Mechanics, 2018, 39(3): 324-333. doi: 10.21656/1000-0887.380089
Citation: ZHANG Yanlong, WANG Li, SHI Jianfei. Bifurcation Evolution of Duffing Systems on 2-Parameter Planes[J]. Applied Mathematics and Mechanics, 2018, 39(3): 324-333. doi: 10.21656/1000-0887.380089

Duffing系统在双参数平面上的分岔演化过程

doi: 10.21656/1000-0887.380089
基金项目: 国家自然科学基金(11302092; 11362008)
详细信息
    作者简介:

    张艳龙(1981—),男,副教授,博士生,硕士生导师(E-mail: zhangyl@mail.lzjtu.cn);王丽(1979—),女,副教授,硕士(通讯作者. E-mail: wangl@lzcu.edu.cn).

  • 中图分类号: O322;O241.1

Bifurcation Evolution of Duffing Systems on 2-Parameter Planes

Funds: The National Natural Science Foundation of China(11302092; 11362008)
  • 摘要: 给出了参数空间上最大Lyapunov指数的计算方法,数值计算了Duffing系统在双参数平面上的最大Lyapunov指数.结合单参数最大Lyapunov指数、分岔图、相图以及时间历程图,讨论了Duffing系统在双参数平面上的分岔以及随系统控制参数变化的分岔演化过程.结果发现在双参数平面上系统发生叉式分岔,出现具有缺边现象的两个不同区域,该区域内系统对初值有较强的敏感性,存在两吸引子共存现象;系统运动经过周期跳跃曲线时振动幅值突然减小;系统外激励频率较小时常引起颤振运动.此外,在两个具有缺边现象的区域内,随刚度系数的不断增加,系统出现了倍周期分岔曲线环,而且倍周期分岔曲线环内不断嵌套新的倍周期分岔曲线环,导致系统最终经倍周期分岔序列进入混沌状态,随着控制参数的变化,系统在双参数平面上的动力学特性变得非常复杂.
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出版历程
  • 收稿日期:  2017-04-07
  • 修回日期:  2017-04-26
  • 刊出日期:  2018-03-15

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