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加性二值噪声激励下Duffing系统的随机分岔

武娟 许勇

武娟, 许勇. 加性二值噪声激励下Duffing系统的随机分岔[J]. 应用数学和力学, 2015, 36(6): 593-599. doi: 10.3879/j.issn.1000-0887.2015.06.003
引用本文: 武娟, 许勇. 加性二值噪声激励下Duffing系统的随机分岔[J]. 应用数学和力学, 2015, 36(6): 593-599. doi: 10.3879/j.issn.1000-0887.2015.06.003
WU Juan, XU Yong. Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises[J]. Applied Mathematics and Mechanics, 2015, 36(6): 593-599. doi: 10.3879/j.issn.1000-0887.2015.06.003
Citation: WU Juan, XU Yong. Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises[J]. Applied Mathematics and Mechanics, 2015, 36(6): 593-599. doi: 10.3879/j.issn.1000-0887.2015.06.003

加性二值噪声激励下Duffing系统的随机分岔

doi: 10.3879/j.issn.1000-0887.2015.06.003
基金项目: 国家自然科学基金(11372247;11102157)
详细信息
    作者简介:

    武娟(1987—),女,陕西人,硕士(通讯作者. E-mail: juanwuxixi@gmail.com).

  • 中图分类号: O322

Stochastic Bifurcations in a Duffing System Driven by Additive Dichotomous Noises

Funds: The National Natural Science Foundation of China(11372247;11102157)
  • 摘要: 研究了Duffing系统在加性二值噪声作用下的随机分岔现象.首先,根据二值噪声的统计特性,推导得到二值噪声状态间的跃迁概率,据此对二值噪声进行了数值模拟.其次,利用四阶Runge-Kutta(龙格-库塔)数值算法得到该系统位移和速率的稳态联合概率密度及位移的稳态概率密度.然后,通过对位移稳态概率密度单双峰结构变化的研究,发现加性二值噪声的状态和强度能够诱导系统产生随机分岔现象.最后,观察到随着系统非对称参数的逐渐变化,系统同样产生了随机分岔现象.
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出版历程
  • 收稿日期:  2014-12-30
  • 修回日期:  2015-03-18
  • 刊出日期:  2015-06-15

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