搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

具有非线性阻尼涨落的线性谐振子的随机共振

田艳 何桂添 罗懋康

引用本文:
Citation:

具有非线性阻尼涨落的线性谐振子的随机共振

田艳, 何桂添, 罗懋康

Stochastic resonance of a linear harmonic oscillator with non-linear damping fluctuation

Tian Yan, He Gui-Tian, Luo Mao-Kang
PDF
导出引用
  • 较之于线性噪声, 非线性噪声更广泛地存在于实际系统中, 但其研究远不能满足实际情况的需要. 针对作为非线性阻尼涨落噪声基本构成成分的二次阻尼涨落噪声, 本文考虑了周期信号与之共同作用下的线性谐振子, 关注这类具有基本意义的阻尼涨落噪声的非线性对系统共振行为的影响. 利用Shapiro-Loginov公式和Laplace变换推导了系统稳态响应振幅的解析表达式, 并分析了稳态响应振幅的共振行为, 且以数值仿真验证了理论分析的有效性. 研究发现: 系统稳态响应振幅关于非线性阻尼涨落噪声系数具有非单调依赖关系, 特别是非线性阻尼涨落噪声比线性阻尼涨落噪声更有助于增强系统对外部周期信号的响应程度; 而且, 非线性阻尼涨落噪声比线性阻尼涨落噪声使得稳态响应振幅关于噪声强度具有更为丰富的共振行为; 同时, 二次阻尼涨落噪声使得稳态响应振幅关于系统频率出现真正的共振现象; 而在这些现象和性质中, 非线性噪声项的非线性性质对共振行为起着关键的作用. 显然, 以二次阻尼涨落作为基本形式引入的非线性阻尼涨落噪声, 可以有助于提高微弱周期信号检测的灵敏度和实现对周期信号的频率估计.
    Although non-linear noise exists far more widely in actual systems than linear noise, the study on non-linear noise is far from meeting the needs of practical situations as yet. The phenomenon of stochastic resonance (SR) is a non-linear cooperative effect which is jointly produced by signal, noise, and system, obviously, it is closely related to the nature of the noise. As a result, the non-linear nature of the non-linear noise has an inevitable impact on the dynamic behavior of a system, so it is of great significance to study the non-linear noise's influence on the dynamic behavior of the system. The linear harmonic oscillator is the most basic model to describe different phenomena in nature, and the quadratic noise is the most basic non-linear noise. In this paper, we consider a linear harmonic oscillator driven by an external periodic force and a quadratic damping fluctuation. For the proposed model, we focus on the effect of non-linear nature of quadratic fluctuation on the system's resonant behavior. Firstly, by the use of the Shapiro-Loginov formula and the Laplace transform technique, the analytical expressions of the first moment and the steady response amplitude of the output signal are obtained. Secondly, by studying the impacts of noise parameters and system intrinsic frequency, the non-monotonic behaviors of the steady response amplitude are found. Finally, numerical simulations are presented to verify the effectiveness of the analytical result. According to the research, we have the following conclusions: (1) The steady response amplitude is a non-monotonic function of coefficients of the quadratic damping fluctuation. Furthermore, the non-linear damping fluctuation is easier to contribute the system's enhancing response to the external periodic signal than the linear fluctuation. (2) The evolution of the steady response amplitude versus noise intensity presents more resonant behaviors. One-peak SR phenomenon and double-peak SR phenomenon are observed at different values of coefficients of the quadratic noise, particularly, the SR phenomenon disappears at the positive quadratic coefficient of the quadratic noise. (3) The evolution of the steady response amplitude versus the system intrinsic frequency presents true resonance, i. e. the phenomenon of resonance appears when the external signal frequency is equal to the system intrinsic frequency. True resonance is not observed in the linear harmonic oscillator driven by a linear damping fluctuation as yet. In conclusion, all the researches show that the non-linear nature of non-linear noise plays a key role in system's resonant behavior, in addition, the non-linear damping fluctuation is conductive to the detection and frequency estimation of weak periodic signal.
      通信作者: 罗懋康, makaluo@scu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11171238)、四川省教育厅科研基金(批准号: 14ZA0050,13ZA0191)、西南石油大学校级科技基金(批准号: 2013XJZ027, 2013XJZ025,2014PYZ015)和西南石油大学青年教师过学术关资助计划(批准号: 201331010049)资助的课题.
      Corresponding author: Luo Mao-Kang, makaluo@scu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238), the Scientific Research Foundation of the Education Department of Sichuan Province, China (Grant Nos. 14ZA0050, 13ZA0191), the Scientific Research Foundation of SWPU of China (Grant Nos. 2013XJZ027, 2013XJZ025, 2014 PYZ015), and the Young Scholars Development Fund of SWPU of China(Grant No. 201331010049).
    [1]

    Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453

    [2]

    Wiesenfeld K, Moss F 1995 Nature 373 33

    [3]

    Gitterman M 2005 Physica A 352 309

    [4]

    Benzi R 2010 Nonlinear Proc. Geophys. 17 431

    [5]

    Gammaitoni L, Hnggi P, Jung P, Marchesoni F 2009 Eur. Phys. J. B 69 1

    [6]

    McDonnell M D, Abbott D 2009 Plos Comput. Biol. 5 e1000348

    [7]

    Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45

    [8]

    Hnggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25

    [9]

    Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223

    [10]

    McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854

    [11]

    Fox R F 1989 Phys. Rev. A 39 4148

    [12]

    Fulinski A 1995 Phys. Rev. E 52 4523

    [13]

    Katrin L, Romi M, Astrid R 2009 Phys. Rev. E 79 051128

    [14]

    Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161

    [15]

    Tian Y, Huang L, Luo M K 2013 Acta Phys. Sin. 62 050502 (in Chinese) [田艳, 黄丽, 罗懋康 2013 物理学报 62 050502]

    [16]

    Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503

    [17]

    Li D S, Li J H 2010 Commun. Theor. Phys. 53 298

    [18]

    Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139

    [19]

    Jiang S Q, Guo F, Zhou Y R, Gu T X 2007 International Conference on Communications, Circuits and Systems Fukuoka, Japan, July 11-13, 2007 p1044

    [20]

    Ning L J, Xu W, Yao M L 2007 Chin. Phys. 16 2595

    [21]

    Zhong S C, Yu T, Zhang L, Ma H 2015 Acta Phys. Sin. 64 020202 (in Chinese) [钟苏川, 蔚涛, 张路, 马洪 2015 物理学报 64 020202]

    [22]

    Zhang L, Zhong S C, Peng H, Luo M K 2011 Chin. Phys. Lett. 28 090505

    [23]

    Gitterman M 2004 Phys. Rev. E 69 041101

    [24]

    Murray S I, Marlan O S, Willis E J 1974 Laser Physics (Rewood City: Addison-Wesley Publishing) p197

    [25]

    Zhang L Y, Cao L, Wu D J 2008 Commun. Theor. Phys. 49 1310

    [26]

    Sancho J M, San Miguel, Drr M D 1982 J. Stat. Phys. 28 291

    [27]

    Sagues F, Migurel S M, Sacho J M 1984 Z. Phys. B 55 269

    [28]

    Hector C, Fernando M, Enrique T 2006 Phys. Rev. E 74 022102

    [29]

    Zhang L, Zhong S C, Peng H, Luo M K 2012 Acta Phys. Sin. 61 130503 (in Chinese) [张路, 钟苏川, 彭皓, 罗懋康 2012 物理学报 61 130503]

    [30]

    Bena I, Broeck C V D, Kawai R, Lindenberg K 2002 Phys. Rev. E 66 045603

    [31]

    Bena I 2006 Int. J. Mod. Phys. B 20 2825

  • [1]

    Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453

    [2]

    Wiesenfeld K, Moss F 1995 Nature 373 33

    [3]

    Gitterman M 2005 Physica A 352 309

    [4]

    Benzi R 2010 Nonlinear Proc. Geophys. 17 431

    [5]

    Gammaitoni L, Hnggi P, Jung P, Marchesoni F 2009 Eur. Phys. J. B 69 1

    [6]

    McDonnell M D, Abbott D 2009 Plos Comput. Biol. 5 e1000348

    [7]

    Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45

    [8]

    Hnggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25

    [9]

    Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223

    [10]

    McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854

    [11]

    Fox R F 1989 Phys. Rev. A 39 4148

    [12]

    Fulinski A 1995 Phys. Rev. E 52 4523

    [13]

    Katrin L, Romi M, Astrid R 2009 Phys. Rev. E 79 051128

    [14]

    Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161

    [15]

    Tian Y, Huang L, Luo M K 2013 Acta Phys. Sin. 62 050502 (in Chinese) [田艳, 黄丽, 罗懋康 2013 物理学报 62 050502]

    [16]

    Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503

    [17]

    Li D S, Li J H 2010 Commun. Theor. Phys. 53 298

    [18]

    Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139

    [19]

    Jiang S Q, Guo F, Zhou Y R, Gu T X 2007 International Conference on Communications, Circuits and Systems Fukuoka, Japan, July 11-13, 2007 p1044

    [20]

    Ning L J, Xu W, Yao M L 2007 Chin. Phys. 16 2595

    [21]

    Zhong S C, Yu T, Zhang L, Ma H 2015 Acta Phys. Sin. 64 020202 (in Chinese) [钟苏川, 蔚涛, 张路, 马洪 2015 物理学报 64 020202]

    [22]

    Zhang L, Zhong S C, Peng H, Luo M K 2011 Chin. Phys. Lett. 28 090505

    [23]

    Gitterman M 2004 Phys. Rev. E 69 041101

    [24]

    Murray S I, Marlan O S, Willis E J 1974 Laser Physics (Rewood City: Addison-Wesley Publishing) p197

    [25]

    Zhang L Y, Cao L, Wu D J 2008 Commun. Theor. Phys. 49 1310

    [26]

    Sancho J M, San Miguel, Drr M D 1982 J. Stat. Phys. 28 291

    [27]

    Sagues F, Migurel S M, Sacho J M 1984 Z. Phys. B 55 269

    [28]

    Hector C, Fernando M, Enrique T 2006 Phys. Rev. E 74 022102

    [29]

    Zhang L, Zhong S C, Peng H, Luo M K 2012 Acta Phys. Sin. 61 130503 (in Chinese) [张路, 钟苏川, 彭皓, 罗懋康 2012 物理学报 61 130503]

    [30]

    Bena I, Broeck C V D, Kawai R, Lindenberg K 2002 Phys. Rev. E 66 045603

    [31]

    Bena I 2006 Int. J. Mod. Phys. B 20 2825

  • [1] 钟苏川, 蔚涛, 张路, 马洪. 具有质量及频率涨落的欠阻尼线性谐振子的随机共振. 物理学报, 2015, 64(2): 020202. doi: 10.7498/aps.64.020202
    [2] 靳艳飞, 李贝. 色关联的乘性和加性色噪声激励下分段非线性模型的随机共振. 物理学报, 2014, 63(21): 210501. doi: 10.7498/aps.63.210501
    [3] 谢文贤, 李东平, 许鹏飞, 蔡力, 靳艳飞. 具有固有频率涨落的记忆阻尼线性系统的随机共振. 物理学报, 2014, 63(10): 100502. doi: 10.7498/aps.63.100502
    [4] 蔚涛, 张路, 罗懋康. 具有涨落质量的线性谐振子的共振行为. 物理学报, 2013, 62(12): 120504. doi: 10.7498/aps.62.120504
    [5] 田祥友, 冷永刚, 范胜波. 一阶线性系统的调参随机共振研究. 物理学报, 2013, 62(2): 020505. doi: 10.7498/aps.62.020505
    [6] 田艳, 黄丽, 罗懋康. 噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响. 物理学报, 2013, 62(5): 050502. doi: 10.7498/aps.62.050502
    [7] 王林泽, 赵文礼, 陈旋. 基于随机共振原理的分段线性模型的理论分析与实验研究. 物理学报, 2012, 61(16): 160501. doi: 10.7498/aps.61.160501
    [8] 张良英, 金国祥, 曹力. 具有频率涨落的简谐力激励下线性谐振子的随机共振. 物理学报, 2012, 61(8): 080502. doi: 10.7498/aps.61.080502
    [9] 张路, 钟苏川, 彭皓, 罗懋康. 乘性二次噪声驱动的线性过阻尼振子的随机共振. 物理学报, 2012, 61(13): 130503. doi: 10.7498/aps.61.130503
    [10] 陆志新, 曹力. 输入方波信号的过阻尼谐振子的随机共振. 物理学报, 2011, 60(11): 110501. doi: 10.7498/aps.60.110501
    [11] 张莉, 刘立, 曹力. 过阻尼谐振子的随机共振. 物理学报, 2010, 59(3): 1494-1498. doi: 10.7498/aps.59.1494
    [12] 宁丽娟, 徐伟. 信号调制下分段噪声驱动的线性系统的随机共振. 物理学报, 2009, 58(5): 2889-2894. doi: 10.7498/aps.58.2889
    [13] 靳艳飞, 胡海岩. 一类线性阻尼振子的随机共振研究. 物理学报, 2009, 58(5): 2895-2901. doi: 10.7498/aps.58.2895
    [14] 郭立敏, 徐 伟, 阮春蕾, 赵 燕. 二值噪声驱动下二阶线性系统的随机共振. 物理学报, 2008, 57(12): 7482-7486. doi: 10.7498/aps.57.7482
    [15] 张良英, 金国祥, 曹 力. 调频信号的单模激光线性模型随机共振. 物理学报, 2008, 57(8): 4706-4711. doi: 10.7498/aps.57.4706
    [16] 张良英, 曹 力, 金国祥. 调幅波的单模激光线性模型随机共振. 物理学报, 2006, 55(12): 6238-6242. doi: 10.7498/aps.55.6238
    [17] 张广军, 徐健学. 非线性动力系统分岔点邻域内随机共振的特性. 物理学报, 2005, 54(2): 557-564. doi: 10.7498/aps.54.557
    [18] 徐 伟, 靳艳飞, 徐 猛, 李 伟. 偏置信号调制下色关联噪声驱动的线性系统的随机共振. 物理学报, 2005, 54(11): 5027-5033. doi: 10.7498/aps.54.5027
    [19] 靳艳飞, 徐 伟, 李 伟, 徐 猛. 具有周期信号调制噪声的线性模型的随机共振. 物理学报, 2005, 54(6): 2562-2567. doi: 10.7498/aps.54.2562
    [20] 康艳梅, 徐健学, 谢 勇. 单模非线性光学系统的弛豫速率与随机共振. 物理学报, 2003, 52(11): 2712-2717. doi: 10.7498/aps.52.2712
计量
  • 文章访问数:  5156
  • PDF下载量:  283
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-11-04
  • 修回日期:  2015-12-14
  • 刊出日期:  2016-03-05

/

返回文章
返回