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非关联噪声驱动的单稳系统的平均首次穿越时间

何成娣 徐伟 岳晓乐

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非关联噪声驱动的单稳系统的平均首次穿越时间

何成娣, 徐伟, 岳晓乐

The mean first-passage time in a mono-stable system driven by uncorrelated noises

He Cheng-Di, Xu Wei, Yue Xiao-Le
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  • 基于非对称双稳系统的理论研究了偏单稳系统的平均首次穿越时间问题,并基于势函数分析了参数对平均首次穿越时间的影响.得出结论:1)当偏稳系数为零时,随着加性噪声强度和参数a的增加,两个方向的平均首次穿越时间相等且均单调减小,2)随着偏稳系数b的增加,势阱的对称性被破坏,粒子由xs1跃迁到xs2的时间线性地减小,而粒子由xs2跃迁到xs1的时间线性地增加.3)随着乘性噪声强度和加性噪声强度比率R的增加,两个方向平均首次穿越时间均单调增加.
    In this paper,the mean first-passage time (MFPT) in a biased mono-stable system is investigated on the basis of the theory used in an asymmetric bistable system. The effects of parameters on MFPT are also analyzed based on the generalized potential function. The results show that, first,with parameter a and additive noise intensity Q increasing,the MFPTs in two directions both decrease on condition that bias parameter b is equal to zero; second,the time in which the particle jumps from xs1 to xs2 linearly decreases while the time in which the particle jumps from xs2 to xs1 linearly increases,owing to the fact that the symmetry of potential well is broken by the increase of bias parameter b; finally,the MFPTs in two directions monotonically increase as the ratio of multiplicative noise intensity to the additive noise intensity increases.
    • 基金项目: 国家自然科学基金(批准号:10872165)资助的课题.
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    [2]

    Wang J,Cao L,Wu D J 2003 Phys. Lett. A 308 23

    [3]

    Jin Y F,Xu W,Ma S J,Li W 2005 Acta Phys. Sin. 54 3480 (in Chinese) [靳艳飞、徐 伟、马少娟、李 伟 2005 物理学报 54 3480]

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    JiaY,Li J R 1996 Phys. Rev. E 53 5764

    [5]

    Ning L J,Xu W,Yang X L 2007 Acta Phys. Sin. 56 25 (in Chinese) [宁丽娟、徐 伟、杨晓丽 2007 物理学报 56 25]

    [6]

    Zhang N M,Xu W,Wang C Q 2007 Acta Phys. Sin. 56 5083 (in Chinese) [张娜敏、徐 伟、王朝庆 2007 物理学报 56 5083]

    [7]

    Jin Y F,Xu W 2005 Chaos,Solitons and Fractals 23 275

    [8]

    Luo X Q,Zhu S Q 2002 Acta Phys. Sin. 51 977 (in Chinese) [罗晓琴、朱士群 2002 物理学报 51 977]

    [9]

    Xie C W,Mei D C 2003 Chin. Phys. 12 1208

    [10]

    Zhang X Y,Xu W 2007 Chin. Phys. 16 0928

    [11]

    Wang Z Q,Xu W,Zhang N M,Li H Q 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆、徐 伟、张娜敏、李海泉 2008 物理学报 57 749]

    [12]

    Zhao Y,Xu W,Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵 燕、徐 伟、邹少存 2009 物理学报 58 1396]

    [13]

    Vilar J M G,Rubi J M 1996 Phys. Rev. Lett. 77 2863

    [14]

    Stocks N G,Stein N D,Soskin S M,McClintock P V E 1992 J. Phys. A:Math. Gen. 25 L1119

    [15]

    Stocks N G,Stein N D,McClintock P V E 1993 J. Phys. A:Math. Gen. 26 L385

    [16]

    Guo F,Zhou Y R,Jiang S Q,Gu T X 2006 J. Phys. A:Math. Gen. 39 13861

    [17]

    Zhou B C,Xu W 2007 Chaos,Solution and Fractals 40 401

    [18]

    Hu G 1994 Stochastic Forces and Nonlinear System (Shanghai:Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡 岗 1994 随机力与非线性系统 (上海:上海科技教育出版社)]

  • [1]

    Madureira A J R,Hanggi P,Wio H S 1996 Phys. Lett. A 271 248

    [2]

    Wang J,Cao L,Wu D J 2003 Phys. Lett. A 308 23

    [3]

    Jin Y F,Xu W,Ma S J,Li W 2005 Acta Phys. Sin. 54 3480 (in Chinese) [靳艳飞、徐 伟、马少娟、李 伟 2005 物理学报 54 3480]

    [4]

    JiaY,Li J R 1996 Phys. Rev. E 53 5764

    [5]

    Ning L J,Xu W,Yang X L 2007 Acta Phys. Sin. 56 25 (in Chinese) [宁丽娟、徐 伟、杨晓丽 2007 物理学报 56 25]

    [6]

    Zhang N M,Xu W,Wang C Q 2007 Acta Phys. Sin. 56 5083 (in Chinese) [张娜敏、徐 伟、王朝庆 2007 物理学报 56 5083]

    [7]

    Jin Y F,Xu W 2005 Chaos,Solitons and Fractals 23 275

    [8]

    Luo X Q,Zhu S Q 2002 Acta Phys. Sin. 51 977 (in Chinese) [罗晓琴、朱士群 2002 物理学报 51 977]

    [9]

    Xie C W,Mei D C 2003 Chin. Phys. 12 1208

    [10]

    Zhang X Y,Xu W 2007 Chin. Phys. 16 0928

    [11]

    Wang Z Q,Xu W,Zhang N M,Li H Q 2008 Acta Phys. Sin. 57 749 (in Chinese) [王朝庆、徐 伟、张娜敏、李海泉 2008 物理学报 57 749]

    [12]

    Zhao Y,Xu W,Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵 燕、徐 伟、邹少存 2009 物理学报 58 1396]

    [13]

    Vilar J M G,Rubi J M 1996 Phys. Rev. Lett. 77 2863

    [14]

    Stocks N G,Stein N D,Soskin S M,McClintock P V E 1992 J. Phys. A:Math. Gen. 25 L1119

    [15]

    Stocks N G,Stein N D,McClintock P V E 1993 J. Phys. A:Math. Gen. 26 L385

    [16]

    Guo F,Zhou Y R,Jiang S Q,Gu T X 2006 J. Phys. A:Math. Gen. 39 13861

    [17]

    Zhou B C,Xu W 2007 Chaos,Solution and Fractals 40 401

    [18]

    Hu G 1994 Stochastic Forces and Nonlinear System (Shanghai:Shanghai Scientific and Technological Education Publishing House) (in Chinese) [胡 岗 1994 随机力与非线性系统 (上海:上海科技教育出版社)]

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  • 文章访问数:  4785
  • PDF下载量:  782
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-09-07
  • 修回日期:  2009-12-07
  • 刊出日期:  2010-04-05

非关联噪声驱动的单稳系统的平均首次穿越时间

  • 1. 西北工业大学应用数学系,西安 710072
    基金项目: 

    国家自然科学基金(批准号:10872165)资助的课题.

摘要: 基于非对称双稳系统的理论研究了偏单稳系统的平均首次穿越时间问题,并基于势函数分析了参数对平均首次穿越时间的影响.得出结论:1)当偏稳系数为零时,随着加性噪声强度和参数a的增加,两个方向的平均首次穿越时间相等且均单调减小,2)随着偏稳系数b的增加,势阱的对称性被破坏,粒子由xs1跃迁到xs2的时间线性地减小,而粒子由xs2跃迁到xs1的时间线性地增加.3)随着乘性噪声强度和加性噪声强度比率R的增加,两个方向平均首次穿越时间均单调增加.

English Abstract

参考文献 (18)

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