Stochastic resonance driven by time-modulated correlated coloured noise sources in a single-mode laser

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity are calculated by the linear approximation. The effects caused by noise self-correlation time τ₁, τ₂ and cross-correlated time τ₃ for stochastic resonance are analysed in two ways: τ₁, τ₂ and τ₃ are taken to be the independent variables and the parameters respectively. The effects of the gain coefficient Γ and loss coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema in the curve of R versus K is reduced with the increase of the gain coefficient Γ.     

二值噪声激励下欠阻尼周期势系统的随机共振

研究了二值噪声和周期信号共同激励下欠阻尼周期势系统的随机共振. 利用随机能量法计算了系统的平均输入能量和平均输出信号的振幅和相位差, 讨论了二值噪声对随机共振的影响. 发现随着噪声强度的增大, 平均输入能量曲线存在一个极小值和一个极大值, 系统出现先抑制后共振的现象; 同时, 系统信噪比曲线随噪声强度的增加出现单峰现象, 说明系统存在随机共振现象.     

Stochastic resonance in periodic potentials driven by colored noise

We studied the motion of an underdamped Brownian particle in a periodic potential subject to a harmonic excitation and a colored noise. The average input energy per period and the phase lag are calculated to quantify the phenomenon of stochastic resonance (SR). The numerical results show that most of the out-of-phase trajectories make a transition to the in-phase state as the temperature increases. And the colored noise delays the transitions between these two dynamical states. The each curve of the average input energy per period and the phase lag versus the temperature exist a mono peak and SR appears in this system. Moreover, the optimal temperature where the SR occurs becomes larger and the region of SR grows wider as the correlation time of colored noise increases.     

Stochastic resonance in the FitzHugh--Nagumo system driven by bounded noise

We investigate stochastic resonance (SR) in the FitzHugh--Nagumo system under combined bounded noise and weak harmonic excitation. Taking a spectral amplification factor as a signal-to-noise ratio, we show numerically that bounded noise can induce SR by adjusting either the intensity of bounded noise or its colour. Moreover, the increase of noise colour can enhance the SR and make the peak of the SR shift toward lower noise intensities, which is more feasible in practice. Since bounded noise is flexible to model random excitation, these findings may have some potential applications in engineering, neuroscience and biology.     

非高斯噪声激励下FitzHugh-Nagumo神经元系统的随机共振

研究了乘性非高斯噪声和加性高斯白噪声共同激励下FitzHugh-Nagumo(FHN) 神经元系统的随机共振问题. 利用路径积分法和两态模型理论, 推导出系统信噪比的表达式. 研究结果表明: 系统参数在不同的取值条件下, FHN神经元模型出现了随机共振和双重随机共振现象. 此外, 非高斯参数q在不同的取值条件下, 乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 非高斯噪声的加入有利于增强FHN神经元系统的信号响应.     

Stochastic resonance in linear system driven by multiplicative and additive noise

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation function and the SR phenomenon appeared. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the asymmetry of multiplicative noise has different effect on signal-to-ratio (SNR) for the first two different forms of SR and the effects of multiplicative noise and additive noise on SNR are different.     

关联噪声驱动的非对称双稳系统的随机共振

运用统一色噪声近似理论和两态模型理论,研究了周期矩形信号和关联的乘性色噪声和加性白噪声驱动的非对称双稳系统的随机共振现象,得到了适合信号任意幅值的信噪比表达式.信噪比是乘性噪声强度、加性噪声强度、乘性噪声自关联时间、噪声耦合强度的非单调函数,所以该双稳系统中出现了随机共振.同时,调节加性噪声强度比调节乘性噪声强度更容易产生随机共振.势阱静态非对称性和噪声之间的耦合强度对信噪比的影响是不同的. 关键词： 非对称双稳系统 随机共振 信噪比 周期矩形信号     

Stochastic resonance in an asymmetric bistable system driven by coloured noises

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises.The approximate Fokker-Planck equation is derived based on the Novikov theorem and the Fox approach.By applying the two-state theory,the expression of the signal-to-noise ratio is obtained in the adiabatic limit.The effects of the noise parameters on signal-to-ratio are discussed.It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.     

Stochastic resonance in time-delayed bistable systems driven by weak periodic signal

We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of the signal. The maximum of SNR decreases with increasing the feedback intensity ?. When ? is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.     

Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Based on the exponential monostable potential, we study an exponential monostable system with time-delayed feedback driven by weak periodic signals and additive Gaussian white noises. The small delay approximation is used to deduce the steady-state probability distribution and the effective potential function is derived. The system parameters l and b, time delay τ, feedback strength β can change the shapes of the potential function. The mean first-passage time (MFPT) is calculated, which plays an extremely important role in the research of particles escape. And the signal-to-noise ratio (SNR) of the system can be obtained by using the adiabatic approximation theory. The phenomenon of stochastic resonance is investigated under different system parameters and time-delayed feedback. The amplitude of SNR can be changed by adjusting the system parameters. When the feedback strength β is positive (or negative), the time delay τ can promote (or suppress) the stochastic resonance phenomenon. The SNR versus the noise intensity D presents the stochastic resonance phenomenon. In addition, the SNR increases non-monotonically with the increasing feedback strength β and the parameter b. Also, the analysis and numerical simulation results of SNR are in good agreement with the formula simulation.     

信号调制下分段噪声驱动的线性系统的随机共振

研究了由乘性和加性噪声的线性组合作为调制噪声的线性系统的随机共振.运用平均法,得到了一、二阶矩和信噪比的精确表达式. 通过分析信噪比,在此系统中发现了真实的随机共振、传统的随机共振和广义随机共振.发现在真实的随机共振中,适当地调整参数,共振和抑制会同时出现.此外,还发现对不同的互关联强度,分别选用乘性和加性噪声作为调制噪声能够提高信噪比. 关键词： 随机共振 信噪比 调制噪声 分段噪声     

乘性二次噪声驱动的线性过阻尼振子的随机共振

针对乘性二次噪声和加性周期调制噪声联合驱动的线性过阻尼振子, 利用随机平均法推导了系统响应的一阶、 二阶稳态矩以及稳态响应振幅和方差的解析表达式. 理论分析和仿真实验均表明这类系统具有比传统的由线性噪声驱动的线性系统更丰富的动力学特性; 当二次噪声的系数满足一定条件时, 系统稳态响应的振幅及方差均存在广义随机共振现象.     

随机外磁场作用下Ising自旋体系的随机共振

通过采用数字仿真手段，研究了经平均场处理的Ising自旋体系在弱确定性周期外场和随机外场（噪声场）混合驱动下的动态响应行为.着重考察了不同强度混合驱动外场作用下，Is ing自旋体系的非平衡动态转变所表现出区别于单纯确定性周期场作用下的新特征——随机 共振.选定体系非平衡动态转变的动态序参量Q为表征参量，系统模拟计算了混合驱动外场在多种参数组合下体系的动态响应特征，高场低温下的非连续动态转变和低场高温下的连续动态转变.模拟计算表明在适当混合驱动外场的作用下，Ising自旋体系具有随机共振现象，并诱发形成非 关键词： Ising自旋体系 随机共振 动态相变 对称性     

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance(SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory(LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density(PSD) and signal-to-noise ratio(SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.     

Stochastic resonance in a monostable system driven by square-wave signal and dichotomous noise

<正>This paper investigates the stochastic resonance in a monostable system driven by square-wave signal,asymmetric dichotomous noise as well as by multiplicative and additive white noise.By the use of the properties of the dichotomous noise,it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition.It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise,and which varies non-monotonously with the intensity of the multiplicative and additive noise as well as the system parameters.Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.     

色噪声驱动下调幅波的单模激光随机共振

对单模激光增益模型的光强方程加入调幅波，用线性化近似方法计算了以e指数形式关联的两色噪声驱动下光强的输出功率谱及信噪比. 结果表明噪声间互关联时间及互关联程度对随机共振影响很大，信噪比随着载波信号频率ω和调制信号频率Ω的变化也和白噪声的变化曲线有很大不同. 关键词： 色噪声 单模激光 随机共振 调幅波     

由加性和乘性噪声驱动的非对称双稳系统的随机共振

根据信噪比理论，研究了由乘性和加性白噪声以及周期矩形信号共同作用的非对称双稳系统的随机共振。推导出了信噪比的解析表达式，并且该表达式适用于任意的信号振幅。数值分析表明乘性噪声强度D和加性噪声强度α对信噪比的影响是不同的：对应于任意的一个非对称系数r的值，SNR-α 曲线比SNR-D曲线更容易出现随机共振。即当系统的双阱不是很不对称的时候，改变加性噪声比改变乘性噪声更容易产生随机共振。此外，势井的非对称性能够减小信噪比。     

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio (SNR) is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.     

Stochastic resonance in a single-well system with exponential potential driven by Levy noise

Noise and potential function are vital to stochastic resonance (SR). This paper attempts to broaden the research of the SR and explore a better potential function. Based on the absolute and exponential potentials, a generalized exponential type single-well potential function is constructed. Then the characteristics of the corresponding exponential type single-well SR (ESR) system driven by Levy noise is analyzed numerically. Firstly, the effects of the characteristic index α, symmetric parameter β and noise intensity D of Levy noise on the input signal to noise ratio (SNRi) are investigated. Then, the effects of system parameters a, b, r and noise intensity D on the resonant output is explored. Finally, the ESR system is applied to the fault characteristic extraction of rolling element bearings. The simulation results show that the SR phenomenon is able to be excited by tuning the parameters a, b, r and D under different values of α and β. The larger b (or a) widens the parameter interval of a (or b) which can induce SR. The ESR system is able to solve the problem that the traditional systems fail to achieve SR due to the improper selection of parameters. In bearing fault detection, the detection effect of the ESR system is superior to the bistable SR system.