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     

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.     

Additive noise in noise-induced nonequilibrium transitions

We study different nonlinear systems which possess noise-induced nonequlibrium transitions and shed light on the role of additive noise in these effects. We find that the influence of additive noise can be very nontrivial: it can induce first- and second-order phase transitions, can change properties of on-off intermittency, or stabilize oscillations. For the Swift-Hohenberg coupling, that is a paradigm in the study of pattern formation, we show that additive noise can cause the formation of ordered spatial patterns in distributed systems. We show also the effect of doubly stochastic resonance, which differs from stochastic resonance, because the influence of noise is twofold: multiplicative noise and coupling induce a bistability of a system, and additive noise changes a response of this noise-induced structure to the periodic driving. Despite the close similarity, we point out several important distinctions between conventional stochastic resonance and doubly stochastic resonance. Finally, we discuss open questions and possible experimental implementations. (c) 2001 American Institute of Physics.     

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     

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.     

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.     

Optimal stochastic enhancement of photoionization

The effect of noise on the nonlinear photoionization of an atom due to a femtosecond pulse is investigated in the framework of the stochastic Schr?dinger equation. A modest amount of white noise results in an enhancement of the net ionization yield by several orders of magnitude, giving rise to a form of quantum stochastic resonance. We demonstrate that this effect is preserved if the white noise is replaced by broadband chaotic light.     

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.     

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.     

Brownian motors and stochastic resonance

We study the transport properties for a walker on a ratchet potential. The walker consists of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the stochastic dynamics of the walker on a ratchet with an external periodic forcing, in the overdamped case. The coupling of the two particles corresponds to a single effective particle, describing the internal degree of freedom, in a bistable potential. This double-well potential is subjected to both a periodic forcing and noise and therefore is able to provide a realization of the phenomenon of stochastic resonance. The main result is that there is an optimal amount of noise where the amplitude of the periodic response of the system is maximum, a signal of stochastic resonance, and that precisely for this optimal noise, the average velocity of the walker is maximal, implying a strong link between stochastic resonance and the ratchet effect.     

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.     

Bridging rate coding and temporal spike coding by effect of noise

It is controversial whether temporal spike coding or rate coding is dominant in the information processing of the brain. We show by a two-layered neural network model with noise that, when noise is small, cortical neurons fire synchronously and intervals of synchronous firing robustly encode the signal information, but that the neurons desynchronize with moderately strong noise to encode waveforms of the signal more accurately. Further increase of noise just deteriorates the encoding. A positive role of noise in the brain is suggested in a meaning different from stochastic resonance, coherence resonance, and deterministic chaos.     

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator

In a system of non-linear chemical reactions called the Brusselator, we show that intrinsic noise can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed.     

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.     

Anisotropic stochastic resonance in the system with a 1/f spectrum

A new behavior of two-dimensional system equations has been discovered upon stochastic resonance: at low frequencies of the harmonic excitation and increasing intensity of the white noise, the motion of the system is limited to two mutually perpendicular directions. In this case we obtain an anisotropic stochastic resonance. With further increase in the intensity of the white noise in the system, one can observe a normal stochastic resonance in which an increase in the intensity of fluctuations in the frequency range measured is blurred by directions.     

Statistically robust evidence of stochastic resonance in human auditory perceptual system

In human perception, exogenous noise is known to yield a masking effect, i.e. an increase of the perceptual threshold relative to a stimulus acting on the same modality. However, somehow counter-intuitively, the opposite mechanism can occasionally occur: a decrease of the perceptual threshold for a non-vanishing, virtuous amount of noise. This mechanism, called stochastic resonance, is deemed to provide important information about the role of noise in the human brain. In this paper, we investigate stochastic resonance in a detection task in the auditory modality. Normal-hearing participants were asked to judge the presence of acoustic stimuli of different intensity and superimposed to different levels of white noise. The matrix-like outcomes of a behavioural experiment were fitted by a two-dimensional, noise-dependent psychometric function. The fit revealed a statistically significant stochastic resonance in 43% of the experimental runs. We conclude that, in the auditory modality, stochastic resonance is a tiny effect that, under conventional circumstances, is largely overrun by standard masking.     

调制与解调用于随机共振的微弱周期信号检测

提出了调制随机共振方法，实现了在大参数条件下从强噪声中检测微弱周期信号.将混于噪声中的较高频率的弱信号经调制变为一差频的低频信号作用于随机共振体系，该低频信号满足绝热近似理论，因而能产生随机共振；再经解调可获得埋于噪声中的原较高频率的弱信号.对埋于噪声中的未知频率，可采用连续改变调制振荡器的频率，以获得一个适当的差频信号输入到随机共振体系，根据输出信号共振谱峰的变化经解调而得待检弱信号的未知频率.该方法应具有较高的应用前景. 关键词： 调制与解调 非线性双稳系统 随机共振 微弱信号检测     

色高斯噪声驱动双稳系统的多重随机共振研究

研究了由色关联乘性和加性色噪声作用下的双稳系统的随机共振问题,在绝热近似条件下得到了信噪比的表达式.通过分析所得的初始条件为 x(0)=x₊ 时的信噪比,发现了单随机共振和多重随机共振现象;分析了噪声强度、噪声关联时间和关联强度对系统信噪比的影响. 关键词： 多重随机共振 信噪比 双稳模型 色关联色噪声     

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/f^α noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.     

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.