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随机Duffing映射的Charlier多项式逼近与分岔研究

张莹 岳晓乐 都琳 王亮 方同

张莹, 岳晓乐, 都琳, 王亮, 方同. 随机Duffing映射的Charlier多项式逼近与分岔研究[J]. 机械科学与技术, 2017, 36(2): 190-195. doi: 10.13433/j.cnki.1003-8728.2017.0205
引用本文: 张莹, 岳晓乐, 都琳, 王亮, 方同. 随机Duffing映射的Charlier多项式逼近与分岔研究[J]. 机械科学与技术, 2017, 36(2): 190-195. doi: 10.13433/j.cnki.1003-8728.2017.0205
Zhang Ying, Yue Xiaole, Du Lin, Wang Liang, Fang Tong. Bifurcation Analysis of Stochastic Duffing Map via Charlier Polynomial Approximation[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(2): 190-195. doi: 10.13433/j.cnki.1003-8728.2017.0205
Citation: Zhang Ying, Yue Xiaole, Du Lin, Wang Liang, Fang Tong. Bifurcation Analysis of Stochastic Duffing Map via Charlier Polynomial Approximation[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(2): 190-195. doi: 10.13433/j.cnki.1003-8728.2017.0205

随机Duffing映射的Charlier多项式逼近与分岔研究

doi: 10.13433/j.cnki.1003-8728.2017.0205
基金项目: 

国家自然科学基金项目(11302171,11672232)与陕西省自然科学基础研究计划资助项目(2016JQ1015)资助

详细信息
    作者简介:

    张莹(1981-),副教授,博士,研究方向为非线性动力学,yingzhang1031@nwpu.edu.cn

Bifurcation Analysis of Stochastic Duffing Map via Charlier Polynomial Approximation

  • 摘要: 在参数随机性影响下,借助Charlier正交多项式逼近,实现了Duffing映射系统的动力学行为和随机分岔研究。为了明确系统的随机特性,首先,对确定性Duffing映射的复杂动力学行为进行分析,明确其动力学行为的发生、发展和变化规律;其次,针对系统随机参数的类型,选取相应的Charlier正交多项式实现对随机Duffing映射的逼近,得到扩阶等价确定性系统,进而运用集合平均响应实现随机分岔行为分析。数值结果表明,受随机因素的影响,倍周期分岔点发生前移;且系统的收敛区域随着随机变量强度的增加而缩小。
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出版历程
  • 收稿日期:  2016-01-17
  • 刊出日期:  2017-02-05

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