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乘性色噪声激励下三稳态van der Pol-Duffing振子随机P-分岔

吴志强 郝颖

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乘性色噪声激励下三稳态van der Pol-Duffing振子随机P-分岔

吴志强, 郝颖

Stochastic P-bifurcations in tri-stable van der Pol-Duffing oscillator with multiplicative colored noise

Wu Zhi-Qiang, Hao Ying
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  • 研究了乘性色噪声作用下三稳态van der Pol-Duffing振子的随机P-分岔问题. 首先应用随机平均法得到系统振动幅值稳态概率密度函数的表达式, 进而应用奇异性理论, 得到刻画随机P-分岔发生的临界参数条件的转迁集以及系统存在的典型稳态概率密度曲线, 并通过Monte-Carlo数值模拟进行了验证. 以此为基础讨论了噪声强度、相关时间、系统线性阻尼系数对随机P-分岔和系统稳态响应行为的影响.
    This article aims at studying the stochastic P-bifurcation of tri-stable van der Pol-Duffing oscillator subjected to multiplicative colored noise. First, the stationary probability density of amplitude is derived by using the stochastic averaging method. Then the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. And the different types of stationary probability densities of amplitude are also obtained, which are in good agreement with the results from Monte-Carlo numerical simulation. Based on these results, the effects of the noise correlation time, noise intensity and linear damping coefficient on the P-bifurcation and the stable response behavior of the system are studied.
    • 基金项目: 国家自然科学基金(批准号: 11172198)、国家自然科学基金(批准号: 11372211) 和国家重点基础研究发展计划(批准号: 2014CB046805)资助的课题.
    • Funds: Project supported by the National Science Foundation of China (Grant Nos. 11172198, 11372211), and the National Basic Research Program of China (Grant No. 2014CB046805).
    [1]

    Zhu W Q 1998 Random Vibration (Beijing: Science Press) p465 (in Chinese) [朱位秋1998 随机振动(北京: 科学出版社)第465页]

    [2]

    Chen L C, Zhu W Q 2010 Chin. J. Appl. Mech. 3 517 (in Chinese) [陈林聪, 朱位秋 2010 应用力学学报 3 517]

    [3]

    Chen L C, Zhu W Q 2011 Int. J. Non-Linear Mech. 46 1324

    [4]

    Rong H W, Wang X D, Xu W, Meng G, Fang T 2005 Acta Phys. Sin. 54 2557 (in Chinese) [戎海武, 王向东, 徐伟, 孟光, 方同 2005 物理学报 54 2557]

    [5]

    Rong H W, Wang X D, Meng G, Xu W, Fang T 2006 Chin. J. Appl. Mech. 27 1373 (in Chinese) [戎海武, 王向东, 孟光, 徐伟, 方同 2006 应用数学和力学 27 1373]

    [6]

    Zakharova A, Vadivasova T, Anishchenko V, Koseska A, Kurths J 2010 Phys. Rev. E 81 011106

    [7]

    Xu Y, Gu R C, Zhang H Q, Xu W, Duan J Q 2011 Phys. Rev. E 83 056215

    [8]

    Gu R C, Xu Y, Hao M L 2011 Acta Phys. Sin. 60 060513 (in Chinese) [顾仁财, 许勇, 郝孟丽 2011 物理学报 60 060513]

    [9]

    Wu Z Q, Hao Y 2013 Sci. Sin.: Physica, Mechanica & Astronomica 43 524 (in Chinese) [吴志强, 郝颖 2013 中国科学:中国科学: 物理学 力学 天文学 43 524]

    [10]

    Hao Y, Wu Z Q 2013 Chin. J. Theor. Appl. Mech. 43 257 (in Chinese) [郝颖, 吴志强 2013 力学学报 43 257]

    [11]

    Christiansen L E, Lehn-Schioler T, Mosekilde E, Gránásy P, Matsushita H 2002 Math. Comput. Simulat. 58 385

    [12]

    Dimitriadis G, Li J 2009 AIAA J. 47 2577

    [13]

    Wu Z Q 2012 Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics Beijing August 19-24, 2012

  • [1]

    Zhu W Q 1998 Random Vibration (Beijing: Science Press) p465 (in Chinese) [朱位秋1998 随机振动(北京: 科学出版社)第465页]

    [2]

    Chen L C, Zhu W Q 2010 Chin. J. Appl. Mech. 3 517 (in Chinese) [陈林聪, 朱位秋 2010 应用力学学报 3 517]

    [3]

    Chen L C, Zhu W Q 2011 Int. J. Non-Linear Mech. 46 1324

    [4]

    Rong H W, Wang X D, Xu W, Meng G, Fang T 2005 Acta Phys. Sin. 54 2557 (in Chinese) [戎海武, 王向东, 徐伟, 孟光, 方同 2005 物理学报 54 2557]

    [5]

    Rong H W, Wang X D, Meng G, Xu W, Fang T 2006 Chin. J. Appl. Mech. 27 1373 (in Chinese) [戎海武, 王向东, 孟光, 徐伟, 方同 2006 应用数学和力学 27 1373]

    [6]

    Zakharova A, Vadivasova T, Anishchenko V, Koseska A, Kurths J 2010 Phys. Rev. E 81 011106

    [7]

    Xu Y, Gu R C, Zhang H Q, Xu W, Duan J Q 2011 Phys. Rev. E 83 056215

    [8]

    Gu R C, Xu Y, Hao M L 2011 Acta Phys. Sin. 60 060513 (in Chinese) [顾仁财, 许勇, 郝孟丽 2011 物理学报 60 060513]

    [9]

    Wu Z Q, Hao Y 2013 Sci. Sin.: Physica, Mechanica & Astronomica 43 524 (in Chinese) [吴志强, 郝颖 2013 中国科学:中国科学: 物理学 力学 天文学 43 524]

    [10]

    Hao Y, Wu Z Q 2013 Chin. J. Theor. Appl. Mech. 43 257 (in Chinese) [郝颖, 吴志强 2013 力学学报 43 257]

    [11]

    Christiansen L E, Lehn-Schioler T, Mosekilde E, Gránásy P, Matsushita H 2002 Math. Comput. Simulat. 58 385

    [12]

    Dimitriadis G, Li J 2009 AIAA J. 47 2577

    [13]

    Wu Z Q 2012 Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics Beijing August 19-24, 2012

计量
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  • PDF下载量:  352
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-03-07
  • 修回日期:  2014-10-18
  • 刊出日期:  2015-03-05

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