Ornstein-Uhlenbeck噪声驱动的过阻尼广义Langevin方程的共振
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摘要
本文研究了受外部周期信号激励的线性过阻尼广义Langevin方程的随机共振现象.本文将系统内噪声建模为指数型关联Ornstein-Uhlenbeck噪声,系统外噪声建模为双态噪声,并利用随机平均法和积分变换算法推导出系统响应的一阶稳态矩和稳态响应振幅的解析表达式.对解析结果的分析表明,该线性过阻尼广义Langevin方程具有丰富的共振行为,即系统的稳态响应振幅随噪声的特征参数、周期激励信号的频率及部分系统参数的变化而出现广义随机共振.
We explore the resonant behavior occurring in an over-damped linear generalized Langevin equation subject to a periodic force.We model the internal noise as an Ornstein-Uhlenbeck noise.The influence of fluctuations of environmental parameter on the system is modeled by a dichotomous noise.Using the stochastic average method and integral transform,we get the exact expressions of the steadystate first moment and amplitude.By studying the impacts of the noise parameters,driving frequency and system parameters,we find that the non-monotonic behaviors of the steady-state output amplitude indicate a lot of resonant behaviors and stochastic resonance(SR)in the wide sense.
We explore the resonant behavior occurring in an over-damped linear generalized Langevin equation subject to a periodic force.We model the internal noise as an Ornstein-Uhlenbeck noise.The influence of fluctuations of environmental parameter on the system is modeled by a dichotomous noise.Using the stochastic average method and integral transform,we get the exact expressions of the steadystate first moment and amplitude.By studying the impacts of the noise parameters,driving frequency and system parameters,we find that the non-monotonic behaviors of the steady-state output amplitude indicate a lot of resonant behaviors and stochastic resonance(SR)in the wide sense.
引文
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[15]Kou S C.Stochastic modeling in nanoscale biophysics:subdiffusion within proteins[J].Ann Appl Stat,2008,2:501.
[16]Kou S C,Xie X S.Generalized Langevin equation with fractional gaussian noise:subdiffusion within a single protein molecule[J].Phys Rev Lett,2004,93:180603.
[17]Gitterman M.Harmonic oscillator with multiplicative noise:nonmonotonic dependence on the strength and the rate of dichotomous noise[J].Phys Rev E,2003,67:057103.
[18]Laio F,Ridolfi L,D’Odorico P.Noise-induced transitions in state-dependent dichotomous processes[J].Phys Rev E,2008,78:031137.
[19]Xu Y,Wu J,Zhang H Q,et al.Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise[J].Nonlinear Dynam,2012,70:531.
[20]Bena I,Van den Broeck C,Kawai R,et al.Nonlinear response with dichotomous noise[J].Phys Rev E,2002,66:045603.
[21]Bena I.Dichotomous markov noise:exact results for out-of-equilibrium systems[J].Int J Mod Phys B,2006,20:2825.
[22]张季谦,辛厚文.噪声在非线性化学体系中作用的研究现状[J].化学进展,2001,13:241.
[23]Shapiro V E,Loginov V M.Formulae of differentiation and their use for solving stochastic equations[J].Physica A,1978,91:563.
[2]Benzi R,Parisi G,Sutera A,et al.Stochastic resonance in climatic change[J].Tellus,1982,34:10.
[3]Nicolis C.Stochastic aspects of climatic transitions response to a periodic forcing[J].Tellus,1982,34:1.
[4]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.
[5]Berdichevsky V,Gitterman M.Stochastic resonance in linear systems subject to multiplicative and additive noise[J].Phys Rev E,1999,60:1494.
[6]Li J H,Han Y X.Phenomenon of stochastic resonance caused by multiplicative asymmetric dichotomous noise[J].Phys Rev E,2006,74:051115.
[7]Gitterman M.Harmonic oscillator with fluctuating damping parameter[J].Phys Rev E,2004,69:041101.
[8]Gitterman M.Classical harmonic oscillator with multiplicative noise[J].Physica A,2005,352:309.
[9]包景东.经典和量子耗散系统的随机模拟方法[M].北京:科学出版社,2009.
[10]龚玉兵,侯中怀,辛厚文.色噪声性质对一氧化氮还原反应体系随机共振的影响[J].高等学校化学学报,2005,26:2331.
[11]Klafter J,Sokolov I M.Anomalous diffusion spreads its wings[J].Phys World,2005,18:29.
[12]Metzler R,Klafter J.The random walk’s guide to anomalous diffusion:a fractional dynamics approach[J].Phys Rep,2000,339:1.
[13]Peter R.Thermally activated escape with potential fluctuations driven by an Ornstein-Uhlenbeck process[J].Phys Rev E,1995,1579:1.
[14]Cabrera J L,Gorronogoitia J,de la Rubia F J.Coherence enhancement in nonlinear systems subject to multiplicative Ornstein-Uhlenbeck noise[J].Phys Rev E,2002,66,022101.
[15]Kou S C.Stochastic modeling in nanoscale biophysics:subdiffusion within proteins[J].Ann Appl Stat,2008,2:501.
[16]Kou S C,Xie X S.Generalized Langevin equation with fractional gaussian noise:subdiffusion within a single protein molecule[J].Phys Rev Lett,2004,93:180603.
[17]Gitterman M.Harmonic oscillator with multiplicative noise:nonmonotonic dependence on the strength and the rate of dichotomous noise[J].Phys Rev E,2003,67:057103.
[18]Laio F,Ridolfi L,D’Odorico P.Noise-induced transitions in state-dependent dichotomous processes[J].Phys Rev E,2008,78:031137.
[19]Xu Y,Wu J,Zhang H Q,et al.Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise[J].Nonlinear Dynam,2012,70:531.
[20]Bena I,Van den Broeck C,Kawai R,et al.Nonlinear response with dichotomous noise[J].Phys Rev E,2002,66:045603.
[21]Bena I.Dichotomous markov noise:exact results for out-of-equilibrium systems[J].Int J Mod Phys B,2006,20:2825.
[22]张季谦,辛厚文.噪声在非线性化学体系中作用的研究现状[J].化学进展,2001,13:241.
[23]Shapiro V E,Loginov V M.Formulae of differentiation and their use for solving stochastic equations[J].Physica A,1978,91:563.