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

非对称双稳耦合网络系统的尺度随机共振研究

孙中奎 鲁捧菊 徐伟

引用本文:
Citation:

非对称双稳耦合网络系统的尺度随机共振研究

孙中奎, 鲁捧菊, 徐伟

System size stochastic resonance in asymmetric bistable coupled network systems

Sun Zhong-Kui, Lu Peng-Ju, Xu Wei
PDF
导出引用
  • 研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象.
    In this paper, the noise-induced dynamics is studied in an asymmetric bistable coupled network system modulated by different signals. According to the Gaussian approximation and the slaving principle, the asymmetric bistable coupled network system is reduced to a low-dimensional model with two potentials, by which the phenomenon of system size stochastic resonance is studied theoretically and numerically. Under the assumption of adiabatic limit, the expressions of signal-to-noise ratio (SNR) are found by virtue of Fokker-Planck equation with respect to cosine signal and rectangle signal, based on which the system size stochastic resonance is investigated. Further, the effects of the noise strength, the asymmetry and the amplitude of the signal on the system size stochastic resonance are well discussed. It is demonstrated that the SNR shows a non-monotonic dependence on the number of coupled systems, which is demonstrated that there is a resonance with respect to the number of coupled systems.
    • 基金项目: 国家自然科学基金(批准号:11272258,11102156)和陕西省青年科技新星和西北工业大学基础研究基金资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272258, 11102156), the Shaanxi Project for Young New Star in Science and Technology and the Northwestern Polytechnical University Foundation for Fundamental Research, China.
    [1]

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

    [2]

    Fauve S, Heslot F 1983 Phys. Lett. A 97 5

    [3]

    McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626

    [4]

    Julicher F, Ajdari A, Prost J 1997 Rev. Mod. Phys. 69 1269

    [5]

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

    [6]

    Li J H 2002 Phys. Rev. E 66 031104

    [7]

    Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123

    [8]

    Wu D, Zhu S Q, Luo X Q, Wu L 2011 Phys. Rev. E 84 021102

    [9]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Phys. Rev. E 80 026206

    [10]

    Sun Z K, Yang X L, Xu W 2012 Phys. Rev. E 85 061125

    [11]

    Sun Z K, Yang X L 2011 Chaos 21 033114

    [12]

    Wu Y, Zhu W Q 2008 Phys. Rev. E 77 041911

    [13]

    Gan C B, Perc M, Wang Q Y 2010 Chin. Phys. B 19 040508

    [14]

    Liu L, Cao L, Zhang L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [刘立, 曹力, 张莉 2010 物理学报 59 1494]

    [15]

    Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501 (in Chinese) [张晓燕, 徐伟, 周丙常 2012 物理学报 61 030501]

    [16]

    Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126

    [17]

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

    [18]

    Gammaitoni L, Marchesoni F, Saetta M E, Santucci S 1989 Phys. Rev. Lett. 62 349

    [19]

    Zhou T, Moss F 1990 Phys. Rev. A 41 4255

    [20]

    Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575

    [21]

    Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 R3321

    [22]

    Heneghan C, Chow C C, Collins J J, Imhoff T T, Lowen S B, Teich M C 1996 Phys. Rev. E 54 R2228

    [23]

    Hu G, Gong D C, Wen X D, Yang C Y, Qing G R, Li R 1992 Phys. Rev. A 46 3250

    [24]

    Li J L, Xu B H 2006 Chin. Phys. 15 2867

    [25]

    Li J L 2007 Chin. Phys. 16 340

    [26]

    Grigorenko A N, Nikitin S I, Roschepkin G V 1997 Phys. Rev. E 56 R4907

    [27]

    Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F 1994 Phys. Rev. Lett. 72 2125

    [28]

    Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775

    [29]

    Masoliver J, Robinson A, Weiss G H 1995 Phys. Rev. E 51 4021

    [30]

    Porra J M 1997 Phys. Rev. E 55 6533

    [31]

    Dhara A K, Mukhopadhyay T 1999 Phys. Rev. E 60 2727

    [32]

    Zhang Y, Hu G, Gammaitoni L 1998 Phys. Rev. E 58 2952

    [33]

    Krawiecki A 2004 Physica A 333 505

    [34]

    Bezrukov S M, Vodyanoy I 1995 Nature 378 362

    [35]

    Morse R P, Roper P 2000 Phys. Rev. E 61 5683

    [36]

    Xu H M, Wang Y 2003 Recent Developments in World Seismology 12 4 (in Chinese) [徐好民, 王煜 2003 国际地震动态 12 4]

    [37]

    Watt D J, Strogatz S H 1998 Nature 393 440

    [38]

    Strogatz S H 2001 Nature 410 268

    [39]

    Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47

    [40]

    Zhu X L, Zhang H T, Sang J P, Huang S Y, Zou X W 2014 Chin. Phys. B 23 068701

    [41]

    Pikovsky A, Zaikin A, la de Casa M A 2002 Phys. Rev. Lett. 88 050601

    [42]

    Schmid G, Goychuk I, Hänggi P 2001 Europhys. Lett. 56 22

    [43]

    Schmid G, Goychuk I, Hänggi P 2004 Phys. Biol. 1 61

    [44]

    Toral R, Mirasso C R, Gunton J D 2003 Europhys. Lett. 61 162

    [45]

    Tessone C J, Toral R 2005 Physica A 351 106

    [46]

    Cubero D 2008 Phys. Rev. E 77 021112

    [47]

    Wu D J, Cao L, Chen L H 1990 Principles and Applications in Synergistics (Wuhan: Huazhong University of Science and Technology Press) pp67-93 (in Chinese) [吴大进, 曹力, 陈立华 1990 协同学原理和应用 (武汉: 华中理工大学出版社) 第67–93页]

    [48]

    Hu G 1991 Phys. Rev. A 43 700

    [49]

    Gerashchenko O V 2003 Tech. Phys. Lett. 29 256

  • [1]

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

    [2]

    Fauve S, Heslot F 1983 Phys. Lett. A 97 5

    [3]

    McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2626

    [4]

    Julicher F, Ajdari A, Prost J 1997 Rev. Mod. Phys. 69 1269

    [5]

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

    [6]

    Li J H 2002 Phys. Rev. E 66 031104

    [7]

    Kang Y M, Xu J X, Xie Y 2003 Phys. Rev. E 68 036123

    [8]

    Wu D, Zhu S Q, Luo X Q, Wu L 2011 Phys. Rev. E 84 021102

    [9]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Phys. Rev. E 80 026206

    [10]

    Sun Z K, Yang X L, Xu W 2012 Phys. Rev. E 85 061125

    [11]

    Sun Z K, Yang X L 2011 Chaos 21 033114

    [12]

    Wu Y, Zhu W Q 2008 Phys. Rev. E 77 041911

    [13]

    Gan C B, Perc M, Wang Q Y 2010 Chin. Phys. B 19 040508

    [14]

    Liu L, Cao L, Zhang L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [刘立, 曹力, 张莉 2010 物理学报 59 1494]

    [15]

    Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501 (in Chinese) [张晓燕, 徐伟, 周丙常 2012 物理学报 61 030501]

    [16]

    Sun Z K, Yang X L, Xiao Y Z, Xu W 2014 Chaos 24 023126

    [17]

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

    [18]

    Gammaitoni L, Marchesoni F, Saetta M E, Santucci S 1989 Phys. Rev. Lett. 62 349

    [19]

    Zhou T, Moss F 1990 Phys. Rev. A 41 4255

    [20]

    Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575

    [21]

    Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 R3321

    [22]

    Heneghan C, Chow C C, Collins J J, Imhoff T T, Lowen S B, Teich M C 1996 Phys. Rev. E 54 R2228

    [23]

    Hu G, Gong D C, Wen X D, Yang C Y, Qing G R, Li R 1992 Phys. Rev. A 46 3250

    [24]

    Li J L, Xu B H 2006 Chin. Phys. 15 2867

    [25]

    Li J L 2007 Chin. Phys. 16 340

    [26]

    Grigorenko A N, Nikitin S I, Roschepkin G V 1997 Phys. Rev. E 56 R4907

    [27]

    Wiesenfeld K, Pierson D, Pantazelou E, Dames C, Moss F 1994 Phys. Rev. Lett. 72 2125

    [28]

    Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775

    [29]

    Masoliver J, Robinson A, Weiss G H 1995 Phys. Rev. E 51 4021

    [30]

    Porra J M 1997 Phys. Rev. E 55 6533

    [31]

    Dhara A K, Mukhopadhyay T 1999 Phys. Rev. E 60 2727

    [32]

    Zhang Y, Hu G, Gammaitoni L 1998 Phys. Rev. E 58 2952

    [33]

    Krawiecki A 2004 Physica A 333 505

    [34]

    Bezrukov S M, Vodyanoy I 1995 Nature 378 362

    [35]

    Morse R P, Roper P 2000 Phys. Rev. E 61 5683

    [36]

    Xu H M, Wang Y 2003 Recent Developments in World Seismology 12 4 (in Chinese) [徐好民, 王煜 2003 国际地震动态 12 4]

    [37]

    Watt D J, Strogatz S H 1998 Nature 393 440

    [38]

    Strogatz S H 2001 Nature 410 268

    [39]

    Albert R, Barabasi A L 2002 Rev. Mod. Phys. 74 47

    [40]

    Zhu X L, Zhang H T, Sang J P, Huang S Y, Zou X W 2014 Chin. Phys. B 23 068701

    [41]

    Pikovsky A, Zaikin A, la de Casa M A 2002 Phys. Rev. Lett. 88 050601

    [42]

    Schmid G, Goychuk I, Hänggi P 2001 Europhys. Lett. 56 22

    [43]

    Schmid G, Goychuk I, Hänggi P 2004 Phys. Biol. 1 61

    [44]

    Toral R, Mirasso C R, Gunton J D 2003 Europhys. Lett. 61 162

    [45]

    Tessone C J, Toral R 2005 Physica A 351 106

    [46]

    Cubero D 2008 Phys. Rev. E 77 021112

    [47]

    Wu D J, Cao L, Chen L H 1990 Principles and Applications in Synergistics (Wuhan: Huazhong University of Science and Technology Press) pp67-93 (in Chinese) [吴大进, 曹力, 陈立华 1990 协同学原理和应用 (武汉: 华中理工大学出版社) 第67–93页]

    [48]

    Hu G 1991 Phys. Rev. A 43 700

    [49]

    Gerashchenko O V 2003 Tech. Phys. Lett. 29 256

  • [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, 71(19): 190501. doi: 10.7498/aps.71.20220909
    [2] 焦尚彬, 杨蓉, 张青, 谢国. α稳定噪声驱动的非对称双稳随机共振现象. 物理学报, 2015, 64(2): 020502. doi: 10.7498/aps.64.020502
    [3] 黄翔东, 丁道贤, 南楠, 王兆华. 基于中国余数定理的欠采样下余弦信号的频率估计. 物理学报, 2014, 63(19): 198403. doi: 10.7498/aps.63.198403
    [4] 彭皓, 钟苏川, 屠浙, 马洪. 线性调频信号激励过阻尼双稳系统的随机共振现象研究. 物理学报, 2013, 62(8): 080501. doi: 10.7498/aps.62.080501
    [5] 高仕龙, 钟苏川, 韦鹍, 马洪. 基于混沌和随机共振的微弱信号检测. 物理学报, 2012, 61(18): 180501. doi: 10.7498/aps.61.180501
    [6] 张莉, 元秀华, 武力. 脉冲信号被噪声调制的单模激光随机共振. 物理学报, 2012, 61(11): 110501. doi: 10.7498/aps.61.110501
    [7] 杨定新, 胡政, 杨拥民. 大参数周期信号随机共振解析. 物理学报, 2012, 61(8): 080501. doi: 10.7498/aps.61.080501
    [8] 张晓燕, 徐伟, 周丙常. 周期矩形信号作用下时滞非对称单稳系统的随机共振. 物理学报, 2012, 61(3): 030501. doi: 10.7498/aps.61.030501
    [9] 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
    [10] 朱光起, 丁珂, 张宇, 赵远. 基于随机共振进行弱信号探测的实验研究. 物理学报, 2010, 59(5): 3001-3006. doi: 10.7498/aps.59.3001
    [11] 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
    [12] 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
    [13] 林 敏, 黄咏梅, 方利民. 耦合双稳系统的随机共振控制. 物理学报, 2008, 57(4): 2048-2052. doi: 10.7498/aps.57.2048
    [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] 林 敏, 方利民, 朱若谷. 双频信号作用下耦合双稳系统的双共振特性. 物理学报, 2008, 57(5): 2638-2642. doi: 10.7498/aps.57.2638
    [16] 董小娟. 含关联噪声与时滞项的非对称双稳系统的随机共振. 物理学报, 2007, 56(10): 5618-5622. doi: 10.7498/aps.56.5618
    [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] 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
    [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] 张家树, 李恒超, 肖先赐. 连续混沌信号的离散余弦变换域二次实时滤波预测. 物理学报, 2004, 53(3): 710-716. doi: 10.7498/aps.53.710
计量
  • 文章访问数:  4889
  • PDF下载量:  395
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-04-05
  • 修回日期:  2014-06-25
  • 刊出日期:  2014-11-05

/

返回文章
返回