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较之于线性噪声, 非线性噪声更广泛地存在于实际系统中, 但其研究远不能满足实际情况的需要. 针对作为非线性阻尼涨落噪声基本构成成分的二次阻尼涨落噪声, 本文考虑了周期信号与之共同作用下的线性谐振子, 关注这类具有基本意义的阻尼涨落噪声的非线性对系统共振行为的影响. 利用Shapiro-Loginov公式和Laplace变换推导了系统稳态响应振幅的解析表达式, 并分析了稳态响应振幅的共振行为, 且以数值仿真验证了理论分析的有效性. 研究发现: 系统稳态响应振幅关于非线性阻尼涨落噪声系数具有非单调依赖关系, 特别是非线性阻尼涨落噪声比线性阻尼涨落噪声更有助于增强系统对外部周期信号的响应程度; 而且, 非线性阻尼涨落噪声比线性阻尼涨落噪声使得稳态响应振幅关于噪声强度具有更为丰富的共振行为; 同时, 二次阻尼涨落噪声使得稳态响应振幅关于系统频率出现真正的共振现象; 而在这些现象和性质中, 非线性噪声项的非线性性质对共振行为起着关键的作用. 显然, 以二次阻尼涨落作为基本形式引入的非线性阻尼涨落噪声, 可以有助于提高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.
[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2] Wiesenfeld K, Moss F 1995 Nature 373 33
[3] Gitterman M 2005 Physica A 352 309
[4] Benzi R 2010 Nonlinear Proc. Geophys. 17 431
[5] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 2009 Eur. Phys. J. B 69 1
[6] McDonnell M D, Abbott D 2009 Plos Comput. Biol. 5 e1000348
[7] Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[8] Hnggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
[9] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[10] McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[11] Fox R F 1989 Phys. Rev. A 39 4148
[12] Fulinski A 1995 Phys. Rev. E 52 4523
[13] Katrin L, Romi M, Astrid R 2009 Phys. Rev. E 79 051128
[14] Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[15] Tian Y, Huang L, Luo M K 2013 Acta Phys. Sin. 62 050502 (in Chinese) [田艳, 黄丽, 罗懋康 2013 物理学报 62 050502]
[16] Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503
[17] Li D S, Li J H 2010 Commun. Theor. Phys. 53 298
[18] Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139
[19] Jiang S Q, Guo F, Zhou Y R, Gu T X 2007 International Conference on Communications, Circuits and Systems Fukuoka, Japan, July 11-13, 2007 p1044
[20] Ning L J, Xu W, Yao M L 2007 Chin. Phys. 16 2595
[21] Zhong S C, Yu T, Zhang L, Ma H 2015 Acta Phys. Sin. 64 020202 (in Chinese) [钟苏川, 蔚涛, 张路, 马洪 2015 物理学报 64 020202]
[22] Zhang L, Zhong S C, Peng H, Luo M K 2011 Chin. Phys. Lett. 28 090505
[23] Gitterman M 2004 Phys. Rev. E 69 041101
[24] Murray S I, Marlan O S, Willis E J 1974 Laser Physics (Rewood City: Addison-Wesley Publishing) p197
[25] Zhang L Y, Cao L, Wu D J 2008 Commun. Theor. Phys. 49 1310
[26] Sancho J M, San Miguel, Drr M D 1982 J. Stat. Phys. 28 291
[27] Sagues F, Migurel S M, Sacho J M 1984 Z. Phys. B 55 269
[28] Hector C, Fernando M, Enrique T 2006 Phys. Rev. E 74 022102
[29] 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 物理学报 61 130503]
[30] Bena I, Broeck C V D, Kawai R, Lindenberg K 2002 Phys. Rev. E 66 045603
[31] Bena I 2006 Int. J. Mod. Phys. B 20 2825
-
[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[2] Wiesenfeld K, Moss F 1995 Nature 373 33
[3] Gitterman M 2005 Physica A 352 309
[4] Benzi R 2010 Nonlinear Proc. Geophys. 17 431
[5] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 2009 Eur. Phys. J. B 69 1
[6] McDonnell M D, Abbott D 2009 Plos Comput. Biol. 5 e1000348
[7] Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[8] Hnggi P, Jung P, Zerbe C, Moss F 1993 J. Stat. Phys. 70 25
[9] Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[10] McNamara B, Wiesenfeld K 1989 Phys. Rev. A 39 4854
[11] Fox R F 1989 Phys. Rev. A 39 4148
[12] Fulinski A 1995 Phys. Rev. E 52 4523
[13] Katrin L, Romi M, Astrid R 2009 Phys. Rev. E 79 051128
[14] Berdichevsky V, Gitterman M 1996 Europhys. Lett. 36 161
[15] Tian Y, Huang L, Luo M K 2013 Acta Phys. Sin. 62 050502 (in Chinese) [田艳, 黄丽, 罗懋康 2013 物理学报 62 050502]
[16] Lin L F, Tian Y, Ma H 2014 Chin. Phys. B 23 080503
[17] Li D S, Li J H 2010 Commun. Theor. Phys. 53 298
[18] Gitterman M, Shapiro I 2011 J. Stat. Phys. 144 139
[19] Jiang S Q, Guo F, Zhou Y R, Gu T X 2007 International Conference on Communications, Circuits and Systems Fukuoka, Japan, July 11-13, 2007 p1044
[20] Ning L J, Xu W, Yao M L 2007 Chin. Phys. 16 2595
[21] Zhong S C, Yu T, Zhang L, Ma H 2015 Acta Phys. Sin. 64 020202 (in Chinese) [钟苏川, 蔚涛, 张路, 马洪 2015 物理学报 64 020202]
[22] Zhang L, Zhong S C, Peng H, Luo M K 2011 Chin. Phys. Lett. 28 090505
[23] Gitterman M 2004 Phys. Rev. E 69 041101
[24] Murray S I, Marlan O S, Willis E J 1974 Laser Physics (Rewood City: Addison-Wesley Publishing) p197
[25] Zhang L Y, Cao L, Wu D J 2008 Commun. Theor. Phys. 49 1310
[26] Sancho J M, San Miguel, Drr M D 1982 J. Stat. Phys. 28 291
[27] Sagues F, Migurel S M, Sacho J M 1984 Z. Phys. B 55 269
[28] Hector C, Fernando M, Enrique T 2006 Phys. Rev. E 74 022102
[29] 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 物理学报 61 130503]
[30] Bena I, Broeck C V D, Kawai R, Lindenberg K 2002 Phys. Rev. E 66 045603
[31] Bena I 2006 Int. J. Mod. Phys. B 20 2825
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