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.     

基于随机共振原理的分段线性模型的理论分析与实验研究

提出了一种分段线性双稳态模型, 推导了模型的解析关系及其输出信噪比, 通过对该模型与连续双稳态模型的对比分析和仿真实验, 证明了该模型的优越性.该模型具有参数之间相互独立、易于调节的特点. 在对模型分析与数值仿真的基础上, 通过电路对强噪声背景下的微弱周期信号检测进行了实验研究. 结果表明分段线性随机共振模型能够有效实现对微弱周期信号的检测, 并能显著增强输出信噪比.     

输入信号和噪声对单模激光随机共振的影响

采用色抽运噪声和实虚部间关联的量子噪声驱动的单模激光损失模型,运用线性化近似方法计算了周期性信号加性输入时激光系统的输出光强信噪比,发现用信噪比与量子噪声实虚部间关联系数的关系曲线描述的随机共振现象.在抽运噪声自关联为短时关联情况下,当信号振幅增大和频率增快、抽运噪声色关联时间增大时,系统的随机共振加强;而噪声强度的增加会削弱系统的随机共振.在抽运噪声自关联为长时关联情况下,当信号振幅增大和量子噪声强度减弱时,系统的随机共振加强;而信号频率、抽运噪声强度、抽运噪声色关联时间的变化对系统随机共振的影响很小.     

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.     

随机共振控制的频率匹配方法

根据非线性双稳系统在噪声和弱周期信号作用下产生随机共振的随机同步条件，提出了随机共振控制的频率匹配方法.理论分析和数值仿真结果表明，随机共振是可控制的，通过控制输入信号的频率和噪声的统计特性，不仅能拓宽产生随机共振的频率范围，而且能增强共振的强度，从而实现有更多的噪声能量转换为信号能量. 关键词： 随机共振 非线性双稳系统 频率匹配 控制     

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.     

A Three-Josephson-Junction Device with Noise

A Gaussian white noise model and a symmetric dichotomous noise model for a three-Josephson-junction device are studied. It is shown that the symmetric noise can produce net voltage (Its corresponding dc current is zero), which sterns from the multiplicative noise,the asymmetry of the potential or the asymmetry of the potential itselt; respectively for the Gaussian white noise model or for the dichotomous noise model. The net voltage is negative,and exhibits a peak with increasing the additive noise strength (the stochastic resonance). The dc current-voltage characteristics are calculated for the two models. In addition, we find that when the dc current is not zero, in some scope the absolute value of the dc voltage versus the additive noise strength also presents the stochastic resonance.     

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.     

基于随机共振进行弱信号探测的实验研究

非线性随机共振系统可利用噪声增强微弱信号检测的能力,为强噪声背景下微弱信号的检测开创了新方法.基于随机共振的基本原理设计了硬件电路系统,并将其应用于检测单频和多频微弱信号;通过输入模拟工程实际的带噪信号,采样所得的输出信号的频谱分析结果表明,利用随机共振技术可从强噪声背景下有效地提取出单频和多频弱信号.多频弱信号的有效提取拓展了基于随机共振原理的弱信号检测技术的应用领域,结合数字滤波处理技术有效地消除了低频噪声对信号识别的影响.基于随机共振的弱信号检测技术在信息识别与信息处理方面具有巨大的潜在的应用价值.     

Stochastic resonance in a financial model

We report on our model study of stochastic resonance in the stock market using numerical simulation and analysis,In the model,we take the interest rate as the external signal,the randomness of traders‘ behaviour as the noise,and the stock price as the output,With computer simulations.we find that the system demonstrates a characteristic of stochastic resonance as noise intensity varies,An analytical explanation is proposed.     

Doubly stochastic resonance

We report the effect of doubly stochastic resonance which appears in nonlinear extended systems if the influence of noise is twofold: A multiplicative noise induces bimodality of the mean field of the coupled network and an independent additive noise governs the dynamic behavior in response to small periodic driving. For optimally selected values of the additive noise intensity stochastic resonance is observed, which is manifested by a maximal coherence between the dynamics of the mean field and the periodic input. Numerical simulations of the signal-to-noise ratio and theoretical results from an effective two state model are in good quantitative agreement.     

Non-Gaussian,non-dynamical stochastic resonance

The classical model revealing stochastic resonance is a motion of an overdamped particle in a double-well fourth order potential when combined action of noise and external periodic driving results in amplifying of weak signals. Resonance behavior can also be observed in non-dynamical systems. The simplest example is a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exists the optimal value of the noise intensity resulting in the “most” periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an α-stable noise. We demonstrate that non-equilibrium α-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

α稳定噪声驱动的非对称双稳随机共振现象

以微弱周期信号激励的非对称双稳系统为模型, 以信噪比增益为指标, 首先针对加性和乘性α 稳定噪声共同作用的随机共振现象展开了研究, 然后针对单独加性α 稳定噪声激励的随机共振现象进行了研究, 探究了α 稳定噪声特征指数α 和对称参数β 分别取不同值时, 系统结构参数a, b, 刻画双稳系统非对称性的偏度r以及α 稳定噪声强度放大系数Q或D对非对称双稳系统共振输出的作用规律. 研究结果表明, 无论在加性和乘性α 稳定噪声共同作用下还是在单独加性α 稳定噪声作用下, 通过调节a和b或者r均可诱导随机共振, 实现微弱信号的检测, 且有多个参数区间与之对应, 这些区间不随α 或β 的变化而变化; 在研究噪声诱导的随机共振现象时发现, 调节噪声强度放大系数也可使系统产生随机共振现象, 且达到共振状态时D的区间也不随α 或β 的变化而变化. 这些结论为α 稳定噪声环境下参数诱导随机共振中系统参数以及噪声诱导随机共振中噪声强度的合理选取提供了依据.     

哺乳动物生理振荡中的最佳内噪声效应

基于哺乳动物生理振子模型，构造了相应的介观随机模型，研究了该系统中内噪声对基因振荡的影响．结果发现通过内噪声随机共振的机制，随机的基因振荡可以在最佳内噪声水平处达到最佳状态．同时，还发现存在一个中间的系统尺度使得随机模型表现出比确定性模型更宽的有效振荡区域，这说明了内噪声增强了体系的鲁帮性．讨论了这些效应可能的生理意义．     

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain--noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.     

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.     

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     

α稳定噪声环境下过阻尼系统中的参数诱导随机共振现象

本文采用随机模拟方法, 研究了过阻尼振子系统在α稳定噪声环境下的参数诱导随机共振现象. 结果表明, 在α噪声环境下, 调节系统参数能够诱导随机共振现象; 而且调节非线性项参数时, 随机共振效果随α稳定噪声的指数的减小而减弱, 但当调节线性项参数时, 随机共振效果则随着α稳定噪声的特征指数的减小而增强. 本文的结论在α稳定噪声环境下, 利用参数诱导随机共振原理进行弱信号检测方面具有重要的理论意义, 并有助于理解不同α稳定噪声对一般随机共振系统的共振效果的影响.     

Synchronization of noisy systems by stochastic signals

We study, in terms of synchronization, the nonlinear response of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level-this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train.