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

田艳; 黄丽; 罗懋康

doi:10.7498/aps.62.050502

摘要

针对由加性、乘性噪声和周期信号共同作用的线性过阻尼系统, 在噪声交叉关联强度受到时间周期调制的情况下,利用随机平均法推导了系统响应的信噪比的解析表达式. 研究发现这类系统比噪声间互不相关或噪声交叉关联强度为常数的线性系统具有更丰富的动力学特性, 系统响应的信噪比随交叉关联调制频率的变化出现周期振荡型随机共振, 噪声的交叉关联参数导致随机共振现象的多样化.噪声交叉关联强度的时间周期调制的引入有利于提高对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.

关键词:

Abstract

For an over-damped linear system subjected to correlated additive and multiplicative noise and a periodic signal, when the cross-correlation intensity between noises is a time-periodic function, the analytical expression of the output signal-to-noise ratio (SNR) is derived by means of the stochastic averaging method. It is found that this system has richer dynamic behaviors than the linear systems in which cross-correlation intensity between noises is constant, that the evolution of the output SNR with the cross-correlation modulation frequency presents periodic oscillation, and that the parameters of cross-correlation intensity between noises diversify the stochastic resonance phenomena.The time-periodic modulation of cross-correlation intensity between noises is conductive to enhancing the sensitivity to weak periodic signal detection and implementing the frequency estimation of weak periodic signal.

Keywords:

stochastic resonance /
periodic oscillation /
cross-correlation intensity between noises /
signal-to-noise ratio

作者及机构信息

1.
四川大学数学学院, 成都 610065

基金项目: 国家自然科学基金(批准号: 11171238)资助的课题.

Authors and contacts

1.
College of Mathematics, Sichuan University, Chengdu 610065, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11171238).

参考文献

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[4]	Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[5]	Denisov S I, Vitrenko A N, Horsthemke W 2003 Phys. Rev. E 68 046132
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[7]	Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[8]	Jin Y F, Xu W 2005 Chaos, Solitons Fractals 23 275
[9]	Wang B, Wu X Q, Shao J H 2009 Acta Phys. Sin. 58 1391 (in Chinese) [王兵, 吴秀清, 邵继红 2009 58 1391]
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[17]	Yang M, Li X L, Wu D J 2012 Acta Phys. Sin. 61 160502 (in Chinese) [杨明, 李香莲, 吴大进 2012 61 160502]
[18]	Zhou Y R 2011 Chin. Phys. B 20 010501
[19]	Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 59 1494]
[20]	Lu Z X, Cao L 2011 Acta Phys. Sin. 60 110501 (in Chinese) [陆志新, 曹力 2011 60 110501]
[21]	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 61 130503]
[22]	Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514 (in Chinese) [张晓燕, 徐伟, 周丙常 2011 60 060514]
[23]	Chen D Y, Wang Z L 2008 Acta Phys. Sin. 57 3333 (in Chinese) [陈德彝, 王忠龙 2008 57 3333]
[24]	Chen D Y, Wang Z L 2009 Acta Phys. Sin. 58 2907 (in Chinese) [陈德彝, 王忠龙 2009 58 2907]
[25]	Chen D Y, Wang Z L 2009 Acta Phys. Sin. 58 1403 (in Chinese) [陈德彝, 王忠龙 2009 58 1403]
[26]	Chen D Y, Zhang L 2009 Chin. Phys. B 18 1755
[27]	Tessone C J, Wio H S 1998 Mod. Phys. Lett. B 12 1195
[28]	Tessone C J, Wio H S, Hänggi P 2000 Phys. Rev. E 62 4623
[29]	Shapiro V E, Loginov V M 1978 Physica A 91 563
[30]	Fulinski A 1995 Acta Phys. Pol. B 26 1131
[31]	Gardiner C W 1983 Handbook of Stochastic Processes (Berlin: Springer) p86
[32]	Kubo R, Toda M, Hashitsume N 1986 Nonequilibrium stastical mechanics Part 2 ( Berlin: Springer)

施引文献

[1]	Benzi R, Sutera A, Vulpiani A 1981 J. phys. A: Math. Gen. 14 L453
[2]	Gitterman M 2005 Physica A 352 309
[3]	Fulinski A, Telejko T 1991 Phys. Lett. A 152 11
[4]	Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[5]	Denisov S I, Vitrenko A N, Horsthemke W 2003 Phys. Rev. E 68 046132
[6]	Ai B Q, Wang X J, Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[7]	Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[8]	Jin Y F, Xu W 2005 Chaos, Solitons Fractals 23 275
[9]	Wang B, Wu X Q, Shao J H 2009 Acta Phys. Sin. 58 1391 (in Chinese) [王兵, 吴秀清, 邵继红 2009 58 1391]
[10]	Wang B, Yan S P, Wu X Q 2009 Acta Phys. Sin. 58 5191 (in Chinese) [王兵, 严少平, 吴秀清 2009 58 5191]
[11]	Yang J H, Liu X B 2010 Acta Phys. Sin. 59 3727 (in Chinese) [杨建华, 刘先斌 2010 59 3727]
[12]	Yang L J, Dai Z C 2012 Acta Phys. Sin. 61 100509 (in Chinese) [杨林静, 戴祖诚 2012 61 100509]
[13]	Ning L J, Xu W, Yao M L 2008 Chin. Phys. B 17 486
[14]	Guo F, Zhou Y R, Jiang S Q, Gu T X 2006 Chin. Phys. 15 947
[15]	Du L C, Mei D C 2009 Chin. Phys. B 18 946
[16]	Xu W, Jin Y F, Xu M, Li W 2005 Acta Phys. Sin. 54 5027 (in Chinese) [徐伟, 靳艳飞, 徐猛, 李伟 2005 54 5027]
[17]	Yang M, Li X L, Wu D J 2012 Acta Phys. Sin. 61 160502 (in Chinese) [杨明, 李香莲, 吴大进 2012 61 160502]
[18]	Zhou Y R 2011 Chin. Phys. B 20 010501
[19]	Zhang L, Liu L, Cao L 2010 Acta Phys. Sin. 59 1494 (in Chinese) [张莉, 刘立, 曹力 2010 59 1494]
[20]	Lu Z X, Cao L 2011 Acta Phys. Sin. 60 110501 (in Chinese) [陆志新, 曹力 2011 60 110501]
[21]	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 61 130503]
[22]	Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 60 060514 (in Chinese) [张晓燕, 徐伟, 周丙常 2011 60 060514]
[23]	Chen D Y, Wang Z L 2008 Acta Phys. Sin. 57 3333 (in Chinese) [陈德彝, 王忠龙 2008 57 3333]
[24]	Chen D Y, Wang Z L 2009 Acta Phys. Sin. 58 2907 (in Chinese) [陈德彝, 王忠龙 2009 58 2907]
[25]	Chen D Y, Wang Z L 2009 Acta Phys. Sin. 58 1403 (in Chinese) [陈德彝, 王忠龙 2009 58 1403]
[26]	Chen D Y, Zhang L 2009 Chin. Phys. B 18 1755
[27]	Tessone C J, Wio H S 1998 Mod. Phys. Lett. B 12 1195
[28]	Tessone C J, Wio H S, Hänggi P 2000 Phys. Rev. E 62 4623
[29]	Shapiro V E, Loginov V M 1978 Physica A 91 563
[30]	Fulinski A 1995 Acta Phys. Pol. B 26 1131
[31]	Gardiner C W 1983 Handbook of Stochastic Processes (Berlin: Springer) p86
[32]	Kubo R, Toda M, Hashitsume N 1986 Nonequilibrium stastical mechanics Part 2 ( Berlin: Springer)

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