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

二值噪声激励下欠阻尼周期势系统的随机共振

马正木 靳艳飞

引用本文:
Citation:

二值噪声激励下欠阻尼周期势系统的随机共振

马正木, 靳艳飞

Stochastic resonance in periodic potential driven by dichotomous noise

Ma Zheng-Mu, Jin Yan-Fei
PDF
导出引用
  • 研究了二值噪声和周期信号共同激励下欠阻尼周期势系统的随机共振. 利用随机能量法计算了系统的平均输入能量和平均输出信号的振幅和相位差, 讨论了二值噪声对随机共振的影响. 发现随着噪声强度的增大, 平均输入能量曲线存在一个极小值和一个极大值, 系统出现先抑制后共振的现象; 同时, 系统信噪比曲线随噪声强度的增加出现单峰现象, 说明系统存在随机共振现象.
    Periodic potential system is widely used in a lot of areas such as biological ratchet model of motor, Josephson junction in the field of physics, engineering mechanics of the damping pendulum model, etc. Meanwhile, in the study of stochastic resonance, noise is crucial for dynamical system evolution. There are mostly colored Gaussian noises with nonzero correlation times in practical problems. Dichotomous noises belong to the color noises, and they have some simple statistical properties. In this paper, we study the motion of a Brownian particle in a periodic potential, driven by both a periodic signal and a dichotomous noise. The periodic potential system is different from the bistable system, so we use multiple indexes to explain the stochastic resonance. We calculate the average input energy of the system and the average output signal amplitude and phase difference by using stochastic energetics. Then we discuss the influences of the dichotomous noise intensity, noise correlation time and asymmetric coefficient of potential energy on the stochastic resonance. The results show that with the increase of the noise correlation time, a minimum value and a maximum value occur on the curve of the average input energy, meanwhile, the phenomenon of resonance appears in the system. With the increase of the noise intensity, the value of noise correlation time becomes greater when the phenomenon of stochastic resonance appears. Therefore, the region of stochastic resonance becomes bigger as the noise intensity or the asymmetry coefficient increases. Moreover, with the increase of the noise intensity, a mono peak is found for the signal-to-noise ratio (SNR) of the system and the stochastic resonance appears in this system. With the increase of the noise intensity, we compare the change of the SNR, the average input energy, and the average output signal amplitude. We find that the values of the amplitudes of the average output signal and SNR are basically the same, while the values of the amplitude of the average input energy of the system are a little different. This is because during the process of periodic signal doing work to the system, noise does work and passive dissipation energy of the system occures. In addition, when the curves of the amplitude of the average output signal and SNR reach their corresponding minimum values, the phase difference between the output signal and input signal is minimal.
      通信作者: 靳艳飞, jinyf@bit.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11272051)资助的课题.
      Corresponding author: Jin Yan-Fei, jinyf@bit.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11272051).
    [1]

    Benzi R, Sutera A, VtllPiana A 1981 J. Phys. A 14 L453

    [2]

    Nicolis C 1982 Tellus 3 312

    [3]

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

    [4]

    Murali K, Sinha S, Ditto W L, Bulsara A R 2009 Phys. Rev. Lett. 102 104101

    [5]

    Zhang L Y, Cao L, Wu D J 2003 Acta Phys. Sin. 52 1174 (in Chinese) [张良英, 曹力, 吴大进 2003 物理学报 52 1174]

    [6]

    Jin Y F, Li B 2014 Acta Phys. Sin. 63 210501 (in Chinese) [靳艳飞, 李贝 2014 物理学报 63 210501]

    [7]

    Fronzoni L, Mannella R 1993 J. Stat. Phys. 70 501

    [8]

    Dan D, Mahato M C, Jayannavar A M 1999 Phys. Rev. E 60 6421

    [9]

    Saikia S, Jayannavar A M, Mahato M C 2011 Phys. Rev. E 83 061121

    [10]

    Saikia S 2014 Physica A 416 411

    [11]

    Liu K H, Jin Y F 2013 Physica A 392 5283

    [12]

    Ai B Q, Chen Q Y, He Y F, Li F G, Zhong W R 2014 Phys. Rev. E 88 062129

    [13]

    Fulinski A 1997 Acta Phys. Pol. B 28 1811

    [14]

    Fulinski A 1995 Phys. Rev. E 52 4523

    [15]

    Rozenfeld R, Neiman A, Schimansky G L 2000 Phys. Rev. E 62 3031

    [16]

    Wozinski A 2006 Acta Phys. Pol. B 37 1677

    [17]

    Xu Y, Wu J, Zhang H Q, Ma S J 2012 Nonlinear Dyn. 70 531

    [18]

    Jin Y F 2015 Chin. Phys. B 24 060502

    [19]

    Jin Y F, Xu W, Li W, Xu M 2005 J. Phys. A 38 3733

    [20]

    Barik D, Ghosh P K, Ray D S 2006 J. Stat. Mech. 3 03010

    [21]

    Xu Y, Jin X Q, Zhang H Q, Yang T T 2013 J. Stat. Phys. 152 753

    [22]

    Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) p221 (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)第221页]

    [23]

    Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 802 (in Chinese) [康艳梅, 徐健学, 谢勇 2003 物理学报 52 802]

  • [1]

    Benzi R, Sutera A, VtllPiana A 1981 J. Phys. A 14 L453

    [2]

    Nicolis C 1982 Tellus 3 312

    [3]

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

    [4]

    Murali K, Sinha S, Ditto W L, Bulsara A R 2009 Phys. Rev. Lett. 102 104101

    [5]

    Zhang L Y, Cao L, Wu D J 2003 Acta Phys. Sin. 52 1174 (in Chinese) [张良英, 曹力, 吴大进 2003 物理学报 52 1174]

    [6]

    Jin Y F, Li B 2014 Acta Phys. Sin. 63 210501 (in Chinese) [靳艳飞, 李贝 2014 物理学报 63 210501]

    [7]

    Fronzoni L, Mannella R 1993 J. Stat. Phys. 70 501

    [8]

    Dan D, Mahato M C, Jayannavar A M 1999 Phys. Rev. E 60 6421

    [9]

    Saikia S, Jayannavar A M, Mahato M C 2011 Phys. Rev. E 83 061121

    [10]

    Saikia S 2014 Physica A 416 411

    [11]

    Liu K H, Jin Y F 2013 Physica A 392 5283

    [12]

    Ai B Q, Chen Q Y, He Y F, Li F G, Zhong W R 2014 Phys. Rev. E 88 062129

    [13]

    Fulinski A 1997 Acta Phys. Pol. B 28 1811

    [14]

    Fulinski A 1995 Phys. Rev. E 52 4523

    [15]

    Rozenfeld R, Neiman A, Schimansky G L 2000 Phys. Rev. E 62 3031

    [16]

    Wozinski A 2006 Acta Phys. Pol. B 37 1677

    [17]

    Xu Y, Wu J, Zhang H Q, Ma S J 2012 Nonlinear Dyn. 70 531

    [18]

    Jin Y F 2015 Chin. Phys. B 24 060502

    [19]

    Jin Y F, Xu W, Li W, Xu M 2005 J. Phys. A 38 3733

    [20]

    Barik D, Ghosh P K, Ray D S 2006 J. Stat. Mech. 3 03010

    [21]

    Xu Y, Jin X Q, Zhang H Q, Yang T T 2013 J. Stat. Phys. 152 753

    [22]

    Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) p221 (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)第221页]

    [23]

    Kang Y M, Xu J X, Xie Y 2003 Acta Phys. Sin. 52 802 (in Chinese) [康艳梅, 徐健学, 谢勇 2003 物理学报 52 802]

  • [1] 王烨花, 何美娟. 高斯色噪声激励下非对称双稳耦合网络系统的随机共振. 物理学报, 2022, 0(0): 0-0. doi: 10.7498/aps.71.20220909
    [2] 彭皓, 任芮彬, 钟扬帆, 蔚涛. 三态噪声激励下分数阶耦合系统的随机共振现象. 物理学报, 2022, 71(3): 030502. doi: 10.7498/aps.71.20211272
    [3] 许鹏飞, 公徐路, 李毅伟, 靳艳飞. 含记忆阻尼函数的周期势系统随机共振. 物理学报, 2022, 71(8): 080501. doi: 10.7498/aps.71.20211732
    [4] 彭皓, 任芮彬, 蔚涛. 三态噪声激励下分数阶耦合系统的随机共振现象研究. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211272
    [5] 谢勇, 刘若男. 过阻尼搓板势系统的随机共振. 物理学报, 2017, 66(12): 120501. doi: 10.7498/aps.66.120501
    [6] 焦尚彬, 孙迪, 刘丁, 谢国, 吴亚丽, 张青. 稳定噪声下一类周期势系统的振动共振. 物理学报, 2017, 66(10): 100501. doi: 10.7498/aps.66.100501
    [7] 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
    [8] 张静静, 靳艳飞. 非高斯噪声激励下FitzHugh-Nagumo神经元系统的随机共振. 物理学报, 2012, 61(13): 130502. doi: 10.7498/aps.61.130502
    [9] 张广丽, 吕希路, 康艳梅. 稳定噪声环境下过阻尼系统中的参数诱导随机共振现象. 物理学报, 2012, 61(4): 040501. doi: 10.7498/aps.61.040501
    [10] 张静静, 靳艳飞. 非高斯噪声驱动下非对称双稳系统的平均首次穿越时间与随机共振研究. 物理学报, 2011, 60(12): 120501. doi: 10.7498/aps.60.120501
    [11] 王宝华, 陆启韶, 吕淑娟. 阈下激励与噪声联合作用下肝细胞系统的内钙时空随机共振问题. 物理学报, 2009, 58(11): 7458-7465. doi: 10.7498/aps.58.7458
    [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] 陈德彝, 王忠龙. 噪声间关联程度的时间周期调制对单模激光随机共振的影响. 物理学报, 2008, 57(6): 3333-3336. doi: 10.7498/aps.57.3333
    [14] 周丙常, 徐 伟. 关联噪声驱动的非对称双稳系统的随机共振. 物理学报, 2008, 57(4): 2035-2040. doi: 10.7498/aps.57.2035
    [15] 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
    [16] 宁丽娟, 徐 伟. 光学双稳系统中的随机共振. 物理学报, 2007, 56(4): 1944-1947. doi: 10.7498/aps.56.1944
    [17] 周丙常, 徐 伟. 周期混合信号和噪声联合激励下的非对称双稳系统的随机共振. 物理学报, 2007, 56(10): 5623-5628. doi: 10.7498/aps.56.5623
    [18] 冷永刚, 王太勇, 郭 焱, 汪文津, 胡世广. 级联双稳系统的随机共振特性. 物理学报, 2005, 54(3): 1118-1125. doi: 10.7498/aps.54.1118
    [19] 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
    [20] 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
计量
  • 文章访问数:  3235
  • PDF下载量:  288
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-07-23
  • 修回日期:  2015-08-26
  • 刊出日期:  2015-12-05

二值噪声激励下欠阻尼周期势系统的随机共振

  • 1. 北京理工大学宇航学院, 北京 100081
  • 通信作者: 靳艳飞, jinyf@bit.edu.cn
    基金项目: 国家自然科学基金(批准号: 11272051)资助的课题.

摘要: 研究了二值噪声和周期信号共同激励下欠阻尼周期势系统的随机共振. 利用随机能量法计算了系统的平均输入能量和平均输出信号的振幅和相位差, 讨论了二值噪声对随机共振的影响. 发现随着噪声强度的增大, 平均输入能量曲线存在一个极小值和一个极大值, 系统出现先抑制后共振的现象; 同时, 系统信噪比曲线随噪声强度的增加出现单峰现象, 说明系统存在随机共振现象.

English Abstract

参考文献 (23)

目录

    /

    返回文章
    返回