噪声交叉关联强度的时间周期调制对线性过阻尼系统的随机共振的影响

针对由加性、乘性噪声和周期信号共同作用的线性过阻尼系统, 在噪声交叉关联强度受到时间周期调制的情况下,利用随机平均法推导了系统响应的信噪比的解析表达式. 研究发现这类系统比噪声间互不相关或噪声交叉关联强度为常数的线性系统具有更丰富的动力学特性, 系统响应的信噪比随交叉关联调制频率的变化出现周期振荡型随机共振, 噪声的交叉关联参数导致随机共振现象的多样化.噪声交叉关联强度的时间周期调制的引入有利于提高对微弱周期信号检测的灵敏度和实现对周期信号的频率估计. 关键词： 随机共振 周期振荡型共振 噪声交叉关联强度 信噪比     

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     

非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

周期混合信号和噪声联合激励下的非对称双稳系统的随机共振

研究了周期混合信号和关联的乘性和加性噪声联合激励下的非对称双稳系统的随机共振现象.运用两态理论,给出了基频和高阶谐频信噪比的理论结果.发现对于基频和高阶谐频情形下均出现随机共振，并且高阶谐频存在抑制现象.同时研究了非对称系数和噪声强度以及噪声之间关联强度对信噪比的影响.     

信号调制下色噪声间关联的周期调制对单模激光随机共振的影响

在色噪声间的关联程度受时间周期调制的激光系统中,研究噪声受信号调制情况下的随机共振.用线性化近似的方法计算了光强关联函数及信噪比.具体讨论信噪比随噪声强度、噪声自关联时间、信号频率以及时间周期调制频率的变化关系.发现一种新的随机共振：信噪比随时间周期调制频率的变化出现周期振荡型随机共振;发现广义随机共振：信噪比随抽运噪声自关联时间的变化、随信号频率的变化出现随机共振;同时也存在典型的信噪比随噪声强度的变化而出现的随机共振.而信噪比随量子噪声自关联时间的变化表现为抑制. 关键词： 信号调制 时间周期调制 噪声间关联程度 周期振荡型随机共振     

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.     

偏置信号调制下色关联噪声驱动的线性系统的随机共振

研究了偏置信号调制下关联分段噪声驱动的过阻尼线性系统的随机共振现象，推导出了一阶矩、二阶矩和信噪比的解析表达式. 通过对信噪比曲线的分析，发现该系统中存在三种不同形式的随机共振：传统的随机共振、真正的随机共振和广义的随机共振. 此外，数值结果还表明，加性噪声能够减弱输出的信噪比，而噪声之间的互相关强度能够使输出的信噪比增强. 关键词： 随机共振 信噪比 偏置信号调制的噪声 分段噪声     

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。     

光学双稳系统中的随机共振

运用绝热近似理论，研究了由加性噪声和乘性噪声及周期信号驱动的光学双稳系统的随机共振现象. 发现该模型中输出信噪比R～随着加性噪声强度D_a的变化曲线中会出现随机共振现象，而信噪比R～随着乘性噪声强度D_m的变化曲线是单调减小的，信噪比曲线中没有出现随机共振现象. 因此，加性噪声和乘性噪声对输出信噪比的影响是不同的. 关键词： 随机共振 信噪比 乘性噪声 加性噪声     

偏置信号调制下噪声关联的周期调制对单模激光随机共振的影响

在噪声受偏置信号调制的情况下,讨论色噪声之间的关联受时间周期调制所驱动的单模激光系统中的随机共振.用线性化近似的方法计算了输出信噪比.具体讨论输出信噪比随噪声自关联时间、噪声强度和偏置信号的变化关系.发现输出信噪比随抽运噪声强度和自关联时间的变化出现随机共振,而偏置信号会降低随机共振的峰值.实际应用中应控制优选偏置信号强度. 关键词： 偏置信号 色噪声 时间周期调制 噪声间关联程度     

Parameter-induced stochastic resonance in an over-damped linear system

Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists.     

Improvement of signal-to-noise ratio by stochastic resonance in sigmoid function threshold systems, demonstrated using a CMOS inverter

Stochastic resonance (SR) has become a well-known phenomenon that can enhance weak periodic signals with the help of noise. SR is an interesting phenomenon when applied to signal processing. Although it has been proven that SR does not always improve the signal-to-noise ratio (SNR), in a strongly nonlinear system such as simple threshold system, SR does in fact improve SNR for noisy pulsed signals at appropriate noise strength. However, even in such cases, when noise is weak, the SNR is degraded. Since the noise strength cannot be known in advance, it is difficult to apply SR to real signal processing. In this paper, we focused on the shape of the threshold at which SR did not degrade the SNR when noise was weak. To achieve output change when noise was weak, we numerically analyzed a sigmoid function threshold system. When the slope around the threshold was appropriate, SNR did not degrade when noise was weak and instead was improved at suitable noise strength. We also demonstrated SNR improvement for noisy pulsed voltages using a CMOS inverter, a very common threshold device. The input-output property of a CMOS inverter resembles the sigmoid function. By inputting the noisy signal voltage to a CMOS inverter, we measured the input and output voltages and analyzed the SNRs. The results showed that SNR was effectively improved over a wide range of noise strengths.     

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.     

非高斯噪声驱动下非对称双稳系统的平均首次穿越时间与随机共振研究

研究了乘性非高斯噪声和加性高斯白噪声共同激励下非对称双稳系统的平均首次穿越时间和随机共振问题. 利用路径积分法和两态模型理论,推导出平均首次穿越时间和信噪比的表达式. 研究结果表明:势阱非对称性对两个不同方向的平均首次穿越时间的影响是不同的. 信噪比是加性噪声强度和势阱非对称性的非单调函数,系统出现了随机共振现象;信噪比是乘性噪声强度的单调函数,没有共振峰出现. 这说明该系统中乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 关键词： 非高斯噪声 非对称双稳系统 平均首次穿越时间 随机共振     

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.     

Stochastic Resonance in a Linear Fractional Langevin Equation

The fractional Langevin equation is derived from the generalized Langevin equation driven by the additive fractional Gaussian noise. We investigate the stochastic resonance (SR) phenomenon in the underdamped linear fractional Langevin equation under the external periodic force and multiplicative symmetric dichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expressions of the amplitude and signal-to-noise ratio (SNR) of the system. By studying the impacts of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude and SNR. The results indicate that the bona fide SR, conventional SR and the wide sense of SR phenomena occur in the proposed linear fractional system.     

Stochastic resonance in a parallel array of linear elements

This paper studies stochastic resonance (SR) phenomenon in a parallel array of linear elements with noise. Employing the signal-to-noise ratio (SNR) theory, it obtains the output SNR, and investigates the effects on the output SNR of the system with signal-independent noise and signal-dependent noise respectively. Numerical results show: the curve of the output SNR is monotone with signal-independent noise; whereas SR appears with signal-dependent noise. Moreover, the output SNR enhances rapidly with the increase of N which is the number of elements in this parallel array linear system. This result may provide smart array of simple linear sensors which are capable of acting as noise-aided amplifiers.     

Effect of inertia mass on the stochastic resonance driven by a multiplicative dichotomous noise

A stochastic system driven by dichotomous noise and periodic signal is investigated in the under-damped case.The exact expressions of output signal amplitude and signal-to-noise ratio(SNR) of the system are derived.Numerical results indicate that the inertial mass greatly affects the output signal amplitude and the SNR.Regardless of whether the noise is symmetric or asymmetric,the inertial mass can influence the phenomenon of stochastic resonance(SR) of the system,leading to two types of resonance phenomenon:one is coherence-resonance-like of the SNR with inertial mass,the other is the SR of the SNR with noise intensity.