具有质量及频率涨落的欠阻尼线性谐振子的随机共振

钟苏川; 蔚涛; 张路; 马洪

doi:10.7498/aps.64.020202

摘要

以往的研究大多考虑线性谐振子模型受频率涨落噪声的影响, 而当布朗粒子处于具有吸附能力的复杂环境时, 粒子质量也存在随机涨落. 因此, 本文研究具有质量及频率涨落两项噪声的二阶欠阻尼线性谐振子模型的随机共振现象. 利用Shapiro-Loginov公式和Laplace变换, 推导了系统响应一阶稳态矩及稳态响应振幅的解析表达式. 并根据稳态响应振幅的解析表达式, 建立了稳态响应振幅关于质量涨落噪声及频率涨落噪声各自的噪声强度能够诱导随机共振现象产生的充分必要条件. 仿真实验表明, 当系统参数满足本文所给出的充分必要条件要求时, 系统稳态响应振幅关于噪声强度的变化曲线具有明显的共振峰, 即此选定参数组合能够诱导系统产生随机共振现象.

关键词:

Abstract

When Brownian particle moves in a viscoelastic medium, the surrounding molecules not only collide with the Brownian particle but also adhere to the Brownian particle randomly, thereby changing the mass of the Brownian particle. We investigate the stochastic resonance phenomenon in an underdamped linear harmonic oscillator with fluctuating mass and fluctuating frequency under an external periodic force. The exact expressions of the first moment and the amplitude of the output signal are obtained by using the Shapiro-Loginov formula and the Laplace transform technique. We establish the necessary and sufficient conditions for the emergence of the stochastic resonance phenomenon induced by the mass fluctuation noise intensity and frequency fluctuation noise intensity. Furthermore, based on the necessary and sufficient conditions, the output amplitude shows a non-monotonic dependence on the noise intensity, which means that the stochastic resonance phenomenon happens.

Keywords:

作者及机构信息

1.
四川大学空天科学与工程学院, 成都 610064;

2.
四川大学数学学院, 成都 610064

基金项目: 国家自然科学基金重点项目(批准号: 11171238)、国家自然科学基金青年科学基金(批准号: 11401405)和四川大学青年教师科研启动基金(批准号:2082604174031)资助的课题.

Authors and contacts

1.
College of Aeronautics and Astronautics, Sichuan University, Chengdu 610064, China;

2.
College of Mathematics, Sichuan University, Chengdu 610064, China

Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 11171238), National Natural Science Foundation for the Youth (Grant No. 11401405) and the Young Teacher Fund of Sichuan Uninversity, China (Grant No. 2082604174031).

参考文献

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2]	Benzi R, Parisi G, Sutera A, Vulpiani A 1982 Tellus 34 10
[3]	Benzi R 2010 Nonlinear Proc. Geophys. 17 431
[4]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 2009 Eur. Phys. J. B 69 1
[5]	McDonnell M D, Abbott D 2009 PLos Comput. Biol. 5 e1000348
[6]	Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[7]	Hänggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
[8]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[9]	McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[10]	Fox R F 1989 Phys. Rev. A 39 4148
[11]	Li J H, Han Y X 2006 Phys. Rev. E 74 051115
[12]	Gitterman M 2004 Phys. Rev. E 69 041101
[13]	Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[14]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494
[15]	Gitterman M 2005 Physica A 352 309
[16]	Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[17]	Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 59 1494]
[18]	Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503
[19]	Guo L M, Xu W, Ruan C L, Zhao Y 2008 Acta Phys. Sin. 57 7482 (in Chinese) [郭立敏, 徐伟, 阮春雷, 赵燕 2008 57 7482]
[20]	Goldhirsch I, Zanetti G 1993 Phys. Rev. Lett. 70 1619
[21]	Blum J, Wurm G, Kempf S, Poppe T 2000 Phys. Rev. Lett. 85 2426
[22]	Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139
[23]	Yu T, Zhang L, Luo M K 2013 Acta Phys. Sin. 62 120504 (in Chinese) [蔚涛, 张路, 罗懋康 2013 62 120504]
[24]	Laas K, Mankin R, Reiter E 2011 Int. J. Mathemat. Models and Methods in Appl. Sci. 5 281
[25]	Bena I, Broeck C V D, Kawai R, Lindenberg K 2002 Phys. Rev. E 66 045603
[26]	Laio F, Ridolfi L, Odorico P D 2008 Phys. Rev. E 78 031137
[27]	Bena I 2006 Int. J. Mod. Phys. B 20 2825
[28]	Shapiro V E, Loginov V M 1978 Physica A 91 563
[29]	Oppenheim A V, Willsky A S, Nawab S H (Translated by Liu S T) 2005 Signals and Systems (9th Ed.) (Xi'an: Prentice Hall) pp128, 471, 497-500 (in Chinese) [奥本海姆 A V 等著, 刘树棠译 2005 信号与系统(第九版) (西安: 西安交通大学出版社)第128, 471, 497–500页]
[30]	Laas K, Mankin R, Rekker A 2009 Phys. Rev. E 79 051128

施引文献

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2]	Benzi R, Parisi G, Sutera A, Vulpiani A 1982 Tellus 34 10
[3]	Benzi R 2010 Nonlinear Proc. Geophys. 17 431
[4]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 2009 Eur. Phys. J. B 69 1
[5]	McDonnell M D, Abbott D 2009 PLos Comput. Biol. 5 e1000348
[6]	Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[7]	Hänggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
[8]	Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[9]	McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[10]	Fox R F 1989 Phys. Rev. A 39 4148
[11]	Li J H, Han Y X 2006 Phys. Rev. E 74 051115
[12]	Gitterman M 2004 Phys. Rev. E 69 041101
[13]	Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[14]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494
[15]	Gitterman M 2005 Physica A 352 309
[16]	Zhang L Y, Jin G X, Cao L, Wang Z Y 2012 Chin. Phys. B 21 120502
[17]	Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 59 1494]
[18]	Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503
[19]	Guo L M, Xu W, Ruan C L, Zhao Y 2008 Acta Phys. Sin. 57 7482 (in Chinese) [郭立敏, 徐伟, 阮春雷, 赵燕 2008 57 7482]
[20]	Goldhirsch I, Zanetti G 1993 Phys. Rev. Lett. 70 1619
[21]	Blum J, Wurm G, Kempf S, Poppe T 2000 Phys. Rev. Lett. 85 2426
[22]	Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139
[23]	Yu T, Zhang L, Luo M K 2013 Acta Phys. Sin. 62 120504 (in Chinese) [蔚涛, 张路, 罗懋康 2013 62 120504]
[24]	Laas K, Mankin R, Reiter E 2011 Int. J. Mathemat. Models and Methods in Appl. Sci. 5 281
[25]	Bena I, Broeck C V D, Kawai R, Lindenberg K 2002 Phys. Rev. E 66 045603
[26]	Laio F, Ridolfi L, Odorico P D 2008 Phys. Rev. E 78 031137
[27]	Bena I 2006 Int. J. Mod. Phys. B 20 2825
[28]	Shapiro V E, Loginov V M 1978 Physica A 91 563
[29]	Oppenheim A V, Willsky A S, Nawab S H (Translated by Liu S T) 2005 Signals and Systems (9th Ed.) (Xi'an: Prentice Hall) pp128, 471, 497-500 (in Chinese) [奥本海姆 A V 等著, 刘树棠译 2005 信号与系统(第九版) (西安: 西安交通大学出版社)第128, 471, 497–500页]
[30]	Laas K, Mankin R, Rekker A 2009 Phys. Rev. E 79 051128

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