Stochastic resonance in an over damped linear oscillator driven by multiplicative dichotomous noise and periodic modulated harmonic noise
ZHANG LU1 , ZHONG Suchuan2
1. College of Mathematics, Sichuan University, Chengdu 610065, China;
2. School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
For an overdamped 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 steadystate response were obtained based on the ShapiroLoginov 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 steadystate 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.
收稿日期: 2017-02-08
出版日期: 2018-06-15
引用本文:
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. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(12): 109-115.
[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