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三稳态Van der Pol-Duffing振子的随机P分岔

郝颖 吴志强

郝颖, 吴志强. 三稳态Van der Pol-Duffing振子的随机P分岔[J]. 力学学报, 2013, 45(2): 257-264. doi: 10.6052/0459-1879-12-169
引用本文: 郝颖, 吴志强. 三稳态Van der Pol-Duffing振子的随机P分岔[J]. 力学学报, 2013, 45(2): 257-264. doi: 10.6052/0459-1879-12-169
Hao Ying, Wu Zhiqiang. STOCHASTIC P-BIFURCATION OF TRI-STABLE VAN DER POL-DUFFING OSCILLATOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(2): 257-264. doi: 10.6052/0459-1879-12-169
Citation: Hao Ying, Wu Zhiqiang. STOCHASTIC P-BIFURCATION OF TRI-STABLE VAN DER POL-DUFFING OSCILLATOR[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(2): 257-264. doi: 10.6052/0459-1879-12-169

三稳态Van der Pol-Duffing振子的随机P分岔

doi: 10.6052/0459-1879-12-169
基金项目: 国家自然科学基金(11172198),教育部博士点基金(2009003211005)和教育部新世纪优秀人才支持计划(NCET-15-0247)资助项目.
详细信息
    通讯作者:

    吴志强,教授,主要研究方向:非线性振动、分岔与混沌,振动与控制.E-mail:zhiqwu@tju.edu.cn

  • 中图分类号: O324

STOCHASTIC P-BIFURCATION OF TRI-STABLE VAN DER POL-DUFFING OSCILLATOR

Funds: The project was supported by the National Natural Science Foundation of China (11172198), Ministry of Education Found for the Dotroal (2009003211005) and the Program for New Century Excellent Talents in University (NCET-15-0247).
  • 摘要: 分析了乘性和加性噪声作用下三稳态Van der Pol-Duffing振子的随机P分岔. 首先用随机平均法得到系统的随机微分方程,求得系统响应幅值的稳态概率密度函数. 然后应用分岔分析的奇异性理论,求得随机P分岔发生的临界参数条件,得到多种定性不同的稳态概率密度曲线. 讨论了2种激励噪声强度和系统阻尼对响应稳态概率密度曲线峰的个数、各峰值相对大小的影响. 通过Monte-Carlo数值模拟对理论计算结果进行了验证.该方法可用于其他系统的随机P分岔分析.

     

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出版历程
  • 收稿日期:  2012-06-04
  • 修回日期:  2012-09-29
  • 刊出日期:  2013-03-18

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