乘性双态噪声和周期调制简谐噪声激励下的线性过阻尼谐振子的随机共振

张路 1,钟苏川 2

振动与冲击 ›› 2018, Vol. 37 ›› Issue (12) : 109-115.

PDF(1179 KB)
PDF(1179 KB)
振动与冲击 ›› 2018, Vol. 37 ›› Issue (12) : 109-115.
论文

乘性双态噪声和周期调制简谐噪声激励下的线性过阻尼谐振子的随机共振

  • 张路 1 , 钟苏川 2
作者信息 +

Stochastic resonance in an over damped linear oscillator driven by multiplicative dichotomous noise and periodic modulated harmonic noise

  • ZHANG LU1  , ZHONG Suchuan2
Author information +
文章历史 +

摘要

本文针对乘性双态噪声和加性周期调制简谐噪声联合作用的线性过阻尼振子,利用Shapiro-Loginov公式推导了系统响应的一阶矩以及稳态响应振幅的解析表达式,得出了稳态幅值关于各种噪声参数出现随机共振的条件。研究表明在一定条件下,系统稳态响应振幅关于各种噪声参数具有非单调依赖关系,即出现了随机共振现象。特别地,简谐噪声和普通白噪声相比,不仅具有传统的刻画指标--噪声强度参数,还具有另外两个新的指标参数,即阻尼参数和频率参数,而通过对这两种参数的调节可以有效控制系统稳态响应振幅的随机共振现象,有助于增强系统对外部周期信号的响应程度,从而提高系统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。

Abstract

For an overdamped linear oscillator driven by multiplicative dichotomous noise and periodic modulated harmonic noise, the exact analytical expression of the first moments and the amplitude of the system steadystate response were obtained based on the ShapiroLoginov formula. Moreover, the conditions of stochastic resonance were also obtained. It is found that when the factors of the noise satisfy certain conditions, the amplitude of the system steadystate response has monotonous dependencies on the noise parameters, i.e., the phenomenon of stochastic resonance appears. In particular, compared with the normal white noise, the intensity, damping, and frequency parameters of the harmonic can be regulated to effectively control the stochastic resonance, and thus enhance the system response to external periodic signal.
 

关键词

随机共振 / 线性过阻尼谐振子 / 简谐噪声 / 双态噪声

引用本文

导出引用
张路 1,钟苏川 2. 乘性双态噪声和周期调制简谐噪声激励下的线性过阻尼谐振子的随机共振[J]. 振动与冲击, 2018, 37(12): 109-115
ZHANG LU1,ZHONG Suchuan2. Stochastic resonance in an over damped linear oscillator driven by multiplicative dichotomous noise and periodic modulated harmonic noise[J]. Journal of Vibration and Shock, 2018, 37(12): 109-115

参考文献

[1] 郑志刚, 耦合非线性系统的时空动力学与合作行为, 北京: 高等教育出版社. 2004.
Zhen Zhi-gang, The space-time dynamic and cooperative behavior of coupled nonlinear systems, Beijing: higher education press. 2004.
[2] Benzi R.,et.al..The mechanism of stochastic resonance. J.Phys.A, 1981, 14: 453.
[3] Fauve S.Heslot.F.Stochastic resonance in a bistable system. Phys. Lett. A,1983, 97: 5-7
[4] Gitterman M.,Classical harmonic oscillator with multiplicative noise. Physical A , 2005. 352: 309-334.
[5] McNamara B,Wiesenfeld K,Theory of stochastic resonance. Phys.Rev.A, 1989. 39: 4854-4869.
[6] Y. Jia, SN Yu,JR Li, Stochastic Resonance in a Bistable System Subject to Multiplicative and Additive Noise. 2000, Phys.Rev. E, 62, 1869-1878.
[7]张金燕,林敏, 二次方分段双稳系统的随机共振特性及其应用, 振动与冲击, 2015, 34(19): 213-223.
ZHANG Jin Yan, LIN Min, Stochastic resonance characteristic of a quadratic segmented bistable system and its application, Journal of vibration and shock, 2015, 34(19): 213-223.
[8] 李晓龙,冷永刚,范胜波,石鹏, 基于非均匀周期采样的随机共振研究,振动与冲击,2011,30(12): 78-84.
Li Xiao-long, LENG yong-gang, Fan Sheng-bo, SHI Peng, Stochastic resonance based on periodic non-uniform sampling, Journal of vibration and shock, 2011,30(12): 78-84.
[9] Fulinski A.,Relaxation, noise-induced, and stochastic resonance driven by non-Markovian dichotomic noise. Phys. Rev. E, 1995. 52(4): 4523-4526.
[10]Berdichevsky V. G. M., Multiplicative stochastic resonance in linear systems analytical solution. Europhys. Lett., 1996. 36(3): 161-165.
[11]Berdichevsky V. G. M., Stochastic resonance in linear system subject to multiplicative and addtive noise. Phys. Rev. E, 1999. 60(2):
1494-1499.
[12]Cao, L., Wu, D.J., Stochastic resonance in a linear system with signal-modulated noise. Europhys. Lett. 2003, 61, 593–598.
[13]Zhang, L., Zhong, S.C, Peng, H. and Luo,M.K., Stochastic Multi-Resonance in a Linear System Driven by Multiplicative Polynomial  
Dichotomous Noise, Chin.Phys.Lett., 2011, 28, 090505.
[14]冷永刚,田祥友, 一阶线性系统随机共振在转子轴故障诊断中的应用研究,振动与冲击, 2014, 33(17): 2-5.
LENG Yong-gang, TIAN Xiang-you, Application of a first-order linear system's stochastic resonance in fault diagnosis of rotor shaft, Journal of vibration and shock, 2014, 33(17): 2-5.
[15]Jin, Y., Xu, W., Xu, M., Fang, T.: Stochastic resonance in linear system due to dichotomous noise modulated by bias signal. J. Phys. A,2005, 38, 3733–3742.
[16]周玉荣,何正友, 相关偏置信号调制噪声和加性噪声驱动线性系统随机共振, 振动与冲击, 2011,30(11):171-174.
ZHOU Yu-rong, HE Zheng-you, Stochastic resonance of a linear system with corelated bias signal-modulated noise and additive noise, 2011,30(11):171-174.
[17]W Zhang,G Di, Stochastic resonance in a harmonic oscillator with damping trichotomous noise, Nonlinear Dynamics, 2014,77, 1589–1595.
[18]Guo F Z. Y. R., Stochastic Resonance in an Over-Damped Bias Linear System with Dichotomous Noise. Chin.Phys.Lett., 2006. 23: 1705.
[19]靳艳飞, 徐伟, 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
Jin YanFei,Xu Wei,Li Wei, Stochastic resonance for bias-signal-modulated noise in a linear system, Acta Physica Sinica, 2005, 54(11):
5027-5033
[20]张路,钟苏川, 彭皓, 罗懋康, 乘性二次噪声驱动的线性过阻尼振子的随机共振, 物理学报, 2012.13 : 130503.
Zhang Lu, Zhong Suchuan, Peng Hao and Luo Maokang, Stochastic resonance in a over-damped linear oscillator driven by multiplicative quadratic noise Acta Physica Sinica, 2012.13 : 130503.
[21]胡岗,随机力与非线性系统,上海教育出版社, 1994.
Hu Gang, stochastic force and nonlinear system, Shanghai Education Press, 1994
[22] Vanden B.C., On the relation between white shot noise, Gaussian white noise, and dichotomic markov process. J.Stat.Phys., 1983. 31(3): 467-483.
[23]包景东,经典和量子耗散系统的随机模拟方法,北京,科学出版社,2009.
Bao Jing-dong, Random simulation method of classical and quantum dissipative system , Beijing, science press, 2009.
[24]宋艳丽, 简谐噪声激励下FitzHugh-Nagumo神经元的动力学行为, 物理学报,2010,59(4):2334-2338.
Song Yan-Li, Dynamical behaviour of FitzHugh-Nagumo neuron model driven by harmonic noise, Acta Physica Sinica, 2010,59(4):2334-2338.
[25] 白占武,宋艳丽,简谐速度噪声与简谐噪声环境中谐振子的动力学共振,物理学报,2007, 56(11): 6220-04.
Bai Zhan-Wu, Song Yan-Li, The dynamical resonance of a harmonic oscillator coupled to a heat bath with harmonic velocity noise and harmonic noise, Acta Physica Sinica, 2007, 56(11): 6220-04.
[26] 付海翔,曹力,吴大进,关联噪声驱动系统的一阶数值模拟算法,计算物理,1999,16(5):481-488.
Fu Haixiang, Cao Li, Wu Dajin, A numerical algorithm of first-order for system driven by correlated noises, Chinese journal of computational physics,1999,16(5):481-488.
[27] V.E.Shapiro and V.M.Loginov, “Formulae of differentiation” and their use for solving stochastic differential equations, Physical A 1979, 91:563-574

PDF(1179 KB)

395

Accesses

0

Citation

Detail

段落导航
相关文章

/