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随机参数作用下参激双势阱Duffing系统的随机动力学行为分析

张莹 都琳 岳晓乐 胡健 方同

张莹, 都琳, 岳晓乐, 胡健, 方同. 随机参数作用下参激双势阱Duffing系统的随机动力学行为分析[J]. 应用数学和力学, 2016, 37(11): 1198-1207. doi: 10.21656/1000-0887.370257
引用本文: 张莹, 都琳, 岳晓乐, 胡健, 方同. 随机参数作用下参激双势阱Duffing系统的随机动力学行为分析[J]. 应用数学和力学, 2016, 37(11): 1198-1207. doi: 10.21656/1000-0887.370257
ZHANG Ying, DU Lin, YUE Xiao-le, HU Jian, FANG Tong. Stochastic Nonlinear Dynamics Analysis of Double-Well Duffing Systems Under Random Parametric Excitations[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1198-1207. doi: 10.21656/1000-0887.370257
Citation: ZHANG Ying, DU Lin, YUE Xiao-le, HU Jian, FANG Tong. Stochastic Nonlinear Dynamics Analysis of Double-Well Duffing Systems Under Random Parametric Excitations[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1198-1207. doi: 10.21656/1000-0887.370257

随机参数作用下参激双势阱Duffing系统的随机动力学行为分析

doi: 10.21656/1000-0887.370257
基金项目: 国家自然科学基金(11302170; 11302171; 11672232);陕西省自然科学基础研究计划资助项目(2016JQ1015)
详细信息
    作者简介:

    张莹(1981—),女,副教授,博士(通讯作者. E-mail: yingzhang1031@nwpu.edu.cn).

  • 中图分类号: O322

Stochastic Nonlinear Dynamics Analysis of Double-Well Duffing Systems Under Random Parametric Excitations

Funds: The National Natural Science Foundation of China(11302170; 11302171; 11672232)
  • 摘要: 基于正交多项式逼近理论,研究了在不同随机参数作用下参激双势阱Duffing系统的随机动力学行为.首先,借助Poincaré(庞加莱)截面分析系统的复杂动力学行为;其次,分别针对系统非线性项系数和阻尼项系数为随机参数的情况,运用正交多项式逼近法,将随机参数Duffing系统转化为与之等价的确定性扩阶系统,并证明其有效性;最后,运用等价确定性扩阶系统的集合平均响应,揭示随机系统的动力学特性,以及随机变量强度变化对系统产生的影响.数值结果表明,对于多吸引子共存情形,参激双势阱Duffing系统在随机非线性项系数影响下,其动力学行为较为稳定,共存吸引子与确定性情形保持一致;而当阻尼系数为随机参数时,随着随机变量强度的增加,部分共存吸引子将发生分岔现象.
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出版历程
  • 收稿日期:  2016-08-18
  • 修回日期:  2016-09-06
  • 刊出日期:  2016-11-15

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