非对称噪声驱动的Langevin谐振子的随机共振
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摘要
本文研究了周期调制噪声和非对称双态噪声联合驱动下的具有频率涨落的谐振子的随机共振.本文的主要工作是通过Shapiro-Logniov公式求解谐振子系统的稳态响应一阶矩的解析表达式,并且推导谐振子系统的稳态响应一阶矩的稳定性条件,进而发现了系统关于不同参数的广义随机共振现象,如双峰共振现象等丰富的动力学行为.
In this paper,we focus on the stochastic resonance behaviors of a Langevin oscillator with fluctuating frequency induced by both periodically modulated noise and asymmetric noise.By using the Shapiro-Loginov formula,analytical expression of the first moment of the stable response is calculated.Then,stable conditions of the first moment are obtained and the stochastic resonance behaviors of the oscillator are elucidated.
In this paper,we focus on the stochastic resonance behaviors of a Langevin oscillator with fluctuating frequency induced by both periodically modulated noise and asymmetric noise.By using the Shapiro-Loginov formula,analytical expression of the first moment of the stable response is calculated.Then,stable conditions of the first moment are obtained and the stochastic resonance behaviors of the oscillator are elucidated.
引文
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[2]章惠全.关于随机共振及双稳态系统在信号检测中作用的研究[D].杭州:浙江大学,2009.
[3]Levin J E,Miller J P.Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance[J].Nature,1996,380:165.
[4]Jia Y,Yu S N,Li J R.Stochastic resonance in a bistable system subject to multiplicative and additive noise[J].Phys Rev E,2000,62:1869.
[5]Berdichevsky V,Gitterman M.Stochastic resonance in linear systems subject to multiplicative and additive noise[J].Phys Rev E,1999,60:1494.
[6]Gitterman M.Harmonic oscillator with fluctuating damping parameter[J].Phys Rev E,2004,69,041101.
[7]张路,钟苏川,彭皓,等.乘性二次噪声驱动的线性过阻尼振子的随机共振[J].物理学报,2012,61,130503.
[8]田祥友,冷永刚,范胜波.一阶线性系统的调参随机共振研究[J].物理学报,2013,62:95.
[9]王传毅,任芮彬,邓科.周期调制噪声驱动的具质量涨落的欠阻尼谐振子的随机共振[J].四川大学学报:自然科学版,2016,53:1183.
[10]赖莉,屠浙,罗懋康.色噪声环境下系统记忆性对分数阶布朗马达合作输运特性的影响[J].四川大学学报:自然科学版,2016,53:705.
[11]Gitterman M.Stochastic oscillator with random mass:New type of Brownian motion[J].Physica A,2014,395:11.
[12]靳艳飞,胡海岩.一类线性阻尼振子的随机共振研究[J].物理学报,2009,58:2895.
[13]林丽烽,王会琦.阻尼涨落对线性过阻尼分数阶振子共振的影响[J].四川大学学报:自然科学版,2014,51:1118.
[14]Ren R B,Luo M K,Deng K.Stochastic resonance in a fractional oscillator driven by multiplicative quadratic noise[J].J Stat Mech-Theory E,2017:023210.
[15]Gitterman M.The noisy oscillator:random mass,frequency,damping[M].New York:World Scientific Press,2013.
[16]Wang J,Cao L,Wo D J.Stochastic multiresonance for periodically modulated noise in a single-mode laser[J].Chinese Physics Lett,2003,20:1217.
[17]陈生潭,郭宝龙,李学武.信号与系统[M].3版.西安:西安电子科技大学出版社,2008.
[18]Shapiro V E,Loginov V M.Formulae of differentiation”and their use for solving stochastic equations[J].Physica A,1978,91:563.
[19]Dykman M I,Luchinsky D G,Mcclintock P V,et al.Stochastic resonance for periodically modulated noise intensity[J].Phys Rev A,1992,46:R1713.
[20]张伟年,杜正东,徐冰.常微分方程.[M].2版.北京:高等教育出版社,2014.