级联双稳Duffing系统的随机共振研究

赖志慧; 冷永刚; 范胜波

doi:10.7498/aps.62.070503

摘要

研究了级联双稳Duffing系统的随机共振特性, 证明级联双稳Duffing系统变尺度系数、阻尼比和级数等参数的适当调节, 不仅可实现大参数信号的级联随机共振, 而且可优化单级双稳Duffing系统的随机共振特征, 即参数调节的级联双稳Duffing系统能实现比单级双稳Duffing系统更好的随机共振输出. 此外, 级联双稳Duffing系统对方波信号具有良好的滤波整形作用, 可用于实现含噪方波信号的波形恢复.

关键词:

Abstract

The stochastic resonance of cascaded bistable Duffing system (CBDS) has been studied in this paper. We have shown that with the appropriate adjustment of the parameters of the CBDS, such as the scale transformation coefficient, the damping ratio and the number of cascaded systems, the CBDS can not only achieve large or small parameter stochastic resonance, but also optimize the stochastic resonance result of a single bistable Duffing system (SBDS). That is, with the parameter adjustment, the stochastic resonance effect of the CBDS is much better than that of the SBDS. Furthermore, the CBDS has excellent filtering and smoothing characters for a square wave signal, which can be applied to the recovery of the square wave signal masked by heavy noise.

Keywords:

作者及机构信息

1.
天津大学机械工程学院, 天津 300072;

2.
天津大学机构理论与装备设计教育部重点实验室, 天津 300072;

3.
天津市非线性动力学与混沌控制重点实验室, 天津 300072

基金项目: 国家自然科学基金(批准号: 51275336)和高等学校博士学科点专项科研基金(批准号: 20120032110001)资助的课题.

Authors and contacts

1.
School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;

2.
Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, China;

3.
Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51275336), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032110001).

参考文献

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[2]	Benzi R, Parisi G, Srutera A, Vulpiana A 1982 Tellus 34 11
[3]	Fauve S, Heslot F 1983 Phys. Lett. 97A 5
[4]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2625
[5]	Hu G 1992 Chin. Phys. Lett. 9 69
[6]	Nicolis C, Nicolis G, Frisch H L 1998 Phys. Lett. A 249 443
[7]	Gong Y F 1998 Phys. Lett. A 243 351
[8]	Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rew. Mod. Phys. 70 223
[9]	Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118 (in Chinese) [冷永刚, 王太勇, 郭焱, 汪文津, 胡世广 2005 54 1118]
[10]	Wang F Z, Wen X D, Li R, Qin G R 1996 Jour. Beijing Normal Uni. (Nature Science) 32 47 (in Chinese) [王辅忠, 温孝东, 李蓉, 秦光戎 1996 北京师范大学学报 (自然科学版) 32 47]
[11]	Lai Z H, Leng Y G, Sun J Q, Fan S B 2012 Acta Phys. Sin. 61 050503 (in Chinese) [赖志慧, 冷永刚, 孙建桥, 范胜波 2012 61 050503]
[12]	Kang Y M, Xu J X, Xie Y 2004 Acta Mech. Sin. 36 247 (in Chinese) [康艳梅, 徐健学, 谢勇 2004 力学学报 36 247]
[13]	Zhang G J, Xu J X, Yao H 2006 Acta Mech. Sin. 38 283 (in Chinese) [张广军, 徐健学, 姚宏 2006 力学学报 38 283]
[14]	Karatzas I Shreve S E 1991 Brownian Motion and Stochastic Calculus (2nd ed) (Berlin: Springer Press)
[15]	Holmes P 1979 Philosophical Transactions of the Royal Soeiety of London Series A London,United Kingdom,October 23,1979 292(1394) p419
[16]	Leng Y G, Lai Z H, Fan S B, Gao Y J 2012 Acta Phys. Sin. 61 230502 (in Chinese) [冷永刚, 赖志慧, 范胜波, 高毓璣 2012 61 230502]
[17]	Hu G 1994 Stochastic Forces and Nonlinear System (Shanghai: Shanghai Science & Technology Education Press) pp222-229 (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222–第229页]
[18]	Leng Y G, Leng Y S, Guo Y 2006 Journal of Sound and Vibration 292 788
[19]	Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese) [冷永刚 2011 60 020503]
[20]	Leng Y G, Wang T Y 2007 Mechanical Systems and Signal Processing 21 138

施引文献

[1]	Beniz R, Sutera A, Vulplana 1981 Phys. A 14 453
[2]	Benzi R, Parisi G, Srutera A, Vulpiana A 1982 Tellus 34 11
[3]	Fauve S, Heslot F 1983 Phys. Lett. 97A 5
[4]	McNamara B, Wiesenfeld K, Roy R 1988 Phys. Rev. Lett. 60 2625
[5]	Hu G 1992 Chin. Phys. Lett. 9 69
[6]	Nicolis C, Nicolis G, Frisch H L 1998 Phys. Lett. A 249 443
[7]	Gong Y F 1998 Phys. Lett. A 243 351
[8]	Gammaitoni L, Hanggi P, Jung P, Marchesoni F 1998 Rew. Mod. Phys. 70 223
[9]	Leng Y G, Wang T Y, Guo Y, Wang W J, Hu S G 2005 Acta Phys. Sin. 54 1118 (in Chinese) [冷永刚, 王太勇, 郭焱, 汪文津, 胡世广 2005 54 1118]
[10]	Wang F Z, Wen X D, Li R, Qin G R 1996 Jour. Beijing Normal Uni. (Nature Science) 32 47 (in Chinese) [王辅忠, 温孝东, 李蓉, 秦光戎 1996 北京师范大学学报 (自然科学版) 32 47]
[11]	Lai Z H, Leng Y G, Sun J Q, Fan S B 2012 Acta Phys. Sin. 61 050503 (in Chinese) [赖志慧, 冷永刚, 孙建桥, 范胜波 2012 61 050503]
[12]	Kang Y M, Xu J X, Xie Y 2004 Acta Mech. Sin. 36 247 (in Chinese) [康艳梅, 徐健学, 谢勇 2004 力学学报 36 247]
[13]	Zhang G J, Xu J X, Yao H 2006 Acta Mech. Sin. 38 283 (in Chinese) [张广军, 徐健学, 姚宏 2006 力学学报 38 283]
[14]	Karatzas I Shreve S E 1991 Brownian Motion and Stochastic Calculus (2nd ed) (Berlin: Springer Press)
[15]	Holmes P 1979 Philosophical Transactions of the Royal Soeiety of London Series A London,United Kingdom,October 23,1979 292(1394) p419
[16]	Leng Y G, Lai Z H, Fan S B, Gao Y J 2012 Acta Phys. Sin. 61 230502 (in Chinese) [冷永刚, 赖志慧, 范胜波, 高毓璣 2012 61 230502]
[17]	Hu G 1994 Stochastic Forces and Nonlinear System (Shanghai: Shanghai Science & Technology Education Press) pp222-229 (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222–第229页]
[18]	Leng Y G, Leng Y S, Guo Y 2006 Journal of Sound and Vibration 292 788
[19]	Leng Y G 2011 Acta Phys. Sin. 60 020503 (in Chinese) [冷永刚 2011 60 020503]
[20]	Leng Y G, Wang T Y 2007 Mechanical Systems and Signal Processing 21 138

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