Input-output gain of collective response in an uncoupled parallel array of saturating dynamical subsystems

We explore the collective response of an uncoupled parallel array of saturating dynamical subsystems to a noisy periodic or random signal. Numerical simulation results show that a parallel array of nonlinear saturating subsystems can enhance the signal transmission via tuning the internal noise intensity and increasing the array size. The input-output gain larger than unity, described by the signal-to-noise ratio for a periodic signal or the correlation coefficient for a random signal, is observed in a form of array stochastic resonance. This stochastic resonance phenomenon can be useful for practical information-processing systems.     

线性调频信号激励过阻尼双稳系统的随机共振现象研究

线性调频信号是工程中常见的一种信号, 由于其为非周期信号, 无法以频域信噪比作为衡量其是否产生随机共振的测量手段, 故鲜有文献研究以线性调频信号为激励信号的随机共振现象. 本文利用线性调频信号在最优分数阶Fourier变换域上的能量聚集性, 首次提出以最优分数阶Fourier变换域上定义的信噪比作为测量手段, 研究了线性调频信号叠加高斯白噪声激励过阻尼双稳系统的随机共振现象, 且发现了以线性调频信号为激励信号时产生的新现象, 即随着信号频率的增大, 随机共振将逐渐减弱, 并给出了合理的解释.仿真的结果与理论分析一致, 验证了本文所提出方法的有效性. 关键词： 线性调频信号 分数阶Fourier变换 随机共振     

脉冲信号被噪声调制的单模激光随机共振

建立了一个脉冲信号受噪声调制的新型的单模激光随机共振模型, 采用线性化近似的方法计算了相应的光强关联函数和系统的输出信噪比, 并详细讨论了相应的随机共振现象. 研究结果表明: 由于噪声调制脉冲信号, 使得单模激光表现出崭新的随机共振现象, 即通过改变脉冲信号周期T来实现抑制或优化输出信噪比的目的.     

Comparison of stochastic resonance in static and dynamical nonlinearities

We compare the stochastic resonance (SR) effects in parallel arrays of static and dynamical nonlinearities via the measure of output signal-to-noise ratio (SNR). For a received noisy periodic signal, parallel arrays of both static and dynamical nonlinearities can enhance the output SNR by optimizing the internal noise level. The static nonlinearity is easily implementable, while the dynamical nonlinearity has more parameters to be tuned, at the risk of not exploiting the beneficial role of internal noise components. It is of interest to note that, for an input signal buried in the external Laplacian noise, we show that the dynamical nonlinearity is superior to the static nonlinearity in obtaining a better output SNR. This characteristic is assumed to be closely associated with the kurtosis of noise distribution.     

基于近似熵测度的自适应随机共振研究

变步长随机共振算法有效解决了绝热近似大参数条件下的弱信号检测问题.基于信号近似熵测度的自适应随机共振，实现了变步长随机共振最优输出的自适应求解.周期信号的近似熵不受其幅值和相位变化的影响，而只与其频率及信噪比有关.因此，按照原始数据的采样条件，构造待检测频率在预定信噪比下的标准信号，并以其近似熵为基准，通过自动调节非线性系统的结构参数和计算步长，求得系统输出的近似熵距离矩阵.该矩阵中的最小值所对应的即为自适应条件下非线性动力系统的最优参数.     

Stochastic Resonance in a Simple Threshold Sensor System with Alpha Stable Noise

We investigate the effect of alpha stable noise on stochastic resonance in a single-threshold sensor system by analytic deduction and stochastic simulation. It is shown that stochastic resonance occurs in the threshold system in alpha stable noise environment, but the resonant effect becomes weakened as the alpha stable index decreases or the skewness parameter of alpha stable distribution increases. In particular, for Cauchy noise a nonlinear relation among the optimal noise deviation parameter, the signal amplitude and the threshold is analytically obtained and illustrated by using the extreme value condition for the output signal-to-noise ratio. The results presented in this communication should have application in signal detection and image restoration in the non-Gaussian noisy environment.     

Stochastic resonance at phase noise in signal transmission

A model is developed for a periodic signal corrupted by an arbitrarily distributed phase noise and transmitted by an arbitrary memoryless system. The model establishes a new form of the phenomenon of stochastic resonance, whereby signal transmission can be enhanced by addition of noise. This is revealed by the standard signal-to-noise ratio of stochastic resonance, which here receives an explicit theoretical expression, and which is shown improvable via noise addition. This model is the first to propose a theory of stochastic resonance with phase noise. It represents a unique framework for further investigations on stochastic resonance and its applications.     

周期矩形信号作用下时滞非对称单稳系统 的随机共振

研究了周期矩形信号对时滞非对称单稳系统随机共振的影响,系统中加入的噪声均为Gauss白噪声.得到了信噪比的解析表达式,通过分析信噪比曲线发现系统存在随机共振现象.数值结果还表明乘性与加性噪声强度对信噪比的影响是不同的,在SNR-D参数平面上共振与抑制共存.在信噪比随着时滞量变化的曲线图上发现,当系统的非对称性|r|取值很大或者乘性与加性噪声强度比D/α小于1时,参数平面上的随机共振现象会消失.     

输入方波信号的过阻尼谐振子的随机共振

计算了在输入方波信号情况下过阻尼谐振子的输出功率谱和信噪比,详细讨论了相应的随机共振现象,并与输入余弦信号情况进行对比.研究发现:它们均出现随机共振现象,且均存在共振和抑制并存的现象.但这一并存现象,在两模型中分别出现于不同的共振曲线. 关键词： 过阻尼谐振子 随机共振 方波信号     

色关联噪声驱动下双模激光随机共振

运用线性近似方法,计算得到了关联色噪声和输入周期信号作用下双模激光增益模型输出信号光强的功率密度谱和信噪比,讨论了信噪比随系统参数的变化关系.研究结果发现:在系统的参数和输入信号的频率满足一定条件时,信噪比不仅随噪声强度变化出现了传统的随机共振现象,还发现其随自饱和系数c2、输入信号频率°及交叉耦合参数b的变化都出现了随机共振.     

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.     

一种单稳随机共振系统信噪比增益的数值研究

采用四阶Runge-Kutta数值求解方法, 发现一种单稳随机共振系统信噪比增益的随机共振现象, 并且在一定的条件下系统信噪比增益大于1.通过调节单稳随机共振系统参数可以改变信噪比增益.本文结果拓展了这类单稳的已有研究范围, 在信号检测与处理以及通信领域有着潜在的应用价值. 关键词： 单稳随机共振 信噪比增益 数值分析 非线性     

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker--Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity $Q$, multiplicative noise intensity $D$, static asymmetry $r$ and delay time $\tau$ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry $r$ can restrain stochastic resonance, and the delay time $\tau $ can enhance stochastic resonance. Moreover, the longer the delay time $\tau $ is, the larger the additive noise intensity $Q$ and the multiplicative noise intensity $D$ are, when the stochastic resonance appears.     

Stochastic resonance and antiresonance in monostable systems

We study characteristics of the output signal in a nonlinear monostable inertial dynamical system with the harmonic signal and Gaussian white noise supplied additively to the input. Several types of monostable systems are examined, and analytical expressions for the output-signal power amplification and signal-to-noise ratio are obtained for such systems for the first time. The main attention is paid to the stochastic resonance and antiresonance phenomena, which manifest themselves as nonmonotonic dependences of the mentioned characteristics on the input-noise intensity. In particular, it is shown for the first time that the output signal-to-noise ratio may have a maximum as a function of the input-noise intensity in a monostable system. This corresponds to the classical definition of stochastic resonance, which earlier was only observed in bistable (multistable) systems. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 10, pp. 899–913, October 2008.     

Neural signal transduction aided by noise in multisynaptic excitatory and inhibitory pathways with saturation

We study the stochastic resonance phenomenon in saturating dynamical models of neural signal transduction, at the synaptic stage, wherein the noise in multipathways enhances the processing of neuronal information integrated by excitatory and inhibitory synaptic currents. For an excitatory synaptic pathway, the additive intervention of an inhibitory pathway reduces the stochastic resonance effect. However, as the number of synaptic pathways increases, the signal transduction is greatly improved for parallel multipathways that feature both excitation and inhibition. The obtained results lead us to the realization that the collective property of inhibitory synapses assists neural signal transmission, and a parallel array of neurons can enhance their responses to multiple synaptic currents by adjusting the contributions of excitatory and inhibitory currents.     

Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.     

Stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal

This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal. A new linear approximation approach is advanced to calculate the signal-to-noise ratio. In the linear approximation only the drift term is linearized, the multiplicative noise term is unchangeable. It is found that there appears not only the standard form of stochastic resonance but also the broad sense of stochastic resonance, especially stochastic multiresonance appears in the curve of signal-to-noise ratio as a function of coupling strength λ between the real and imaginary parts of the pump noise.