三稳态Van der Pol-Duffing振子的随机P分岔

郝颖; 吴志强

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

郝颖,
吴志强^,

天津大学机械工程学院力学系,天津300072

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
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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

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

Hao Ying,
Wu Zhiqiang^,

Department of Mechanics, Tianjin University, Tianjin 300072, China

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

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.
- 随机P分岔 /
- 概率密度函数 /
- 奇异性理论
Abstract: This paper aims to investigate the stochastic P-bifurcations in the tri-stable Van der Pol-Duffing oscillator with additive and multiplicative Gauss noise. By using the stochastic averaging method, the stationary probability density function of amplitude is obtained. Then based on the singularity theory of the deterministic system, the explicit parameter conditions for P-bifurcation are deduced, and eleven types of qualitatively different probability density curves are founded. Finally the effects of three coe cients, one for linear damping and two for random excitation strength, are discussed. The results are verified by Monte-Carlo numerical simulations. The method used here is also suitable for other systems' P-bifurcation analysis.
- stochastic P-bifurcation /
- probability density function /
- singularity theory

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