一类非线性神经网络中噪声改善信息传输

以互信息为测度,通过数值计算和计算机仿真比较详细地讨论了在加性和乘性噪声共同作用下的一类非线性神经网络中噪声改善信息传输的(阈上)随机共振现象.在一定的系统阈值和固定的乘性(或加性)噪声强度下,互信息随着加性(或乘性)噪声强度的增加显示出上凸变化,(阈上)随机共振出现;系统阈值单元数目的增加可增强信息传输的效果;系统阈值的增加使得信号处在阈下的成分增多,(阈上)随机共振现象更容易发生.另外,改变加性噪声强度比改变乘性强度时(阈上)随机共振更容易发生.以上结果说明(阈上)随机共振现象的存在性和噪声改善信息传输的效果与乘性或加性噪声强度、阈值单元数以及系统阈值水平密切相关.     

二维映射神经元模型中频率依赖的随机共振

通过数值模拟方法, 研究了在具有稳定次阈值振荡特性的二维映射神经元体系中, 噪声对体系非线性动力学的调控作用. 通过计算发现了噪声诱导的动作电位和随机共振现象. 另外,还研究了体系的控制参数及输入信号的频率对体系动力学的影响, 发现了该体系中频率依赖的随机共振现象. 关键词： 二维映射神经元模型 次阈值振荡 高斯白噪声 随机共振     

双稳态系统中随机共振和相干共振的相关性

研究了加性噪声和乘性噪声共同驱动的双稳态系统中的随机共振和相干共振现象. 针对加性噪声和乘性噪声之间不存在关联性和存在关联性两种情形, 引入一种适当的能同时表征随机共振和相干共振的指标, 应用一阶欧拉方法, 通过数值模拟对系统的随机共振和相干共振现象进行研究. 结果表明在弱噪声驱动下, 随着加性噪声强度的增加, 当系统出现相干共振时, 如果给系统外加一个弱周期驱动力, 几乎在同一时刻, 系统也出现了随机共振现象; 但随着乘性噪声强度的增加, 仅当加性噪声和乘性噪声之间相关时, 此结论成立. 并且系统参数对相干共振和随机共振的影响是一致的. 关键词： 双稳态系统 随机共振 相干共振     

单模激光系统随机共振的模拟研究

用数值模拟方法对具有调制信号的单模激光系统进行了研究, 分析了在阈值附近和远离阈值两种工作方式下的输出信噪比、输出信号功率、 背景噪声功率,并与线性化近似结果进行了对比. 研究发现,激光在阈值附近工作时,输出信噪比会随着量子 噪声的增大出现随机共振现象,这一现象不要求泵噪声与量子噪 声存在关联,但噪声之间的关联会进一步增大信噪比;在远离阈值时, 只有噪声间存在关联时才会发生随机共振现象.研究还发现噪声也 会影响输出信号的功率.     

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     

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.     

色关联的乘性和加性色噪声激励下分段非线性模型的随机共振

研究了色关联的乘性和加性高斯色噪声与外周期信号共同激励下,分段非线性系统的随机共振.利用一致有色噪声近似和两态模型理论,推导出系统稳态概率密度和信噪比的解析表达式,分析了色噪声和周期信号对随机共振的影响,发现系统中存在传统的随机共振和真实的随机共振现象.同时,系统的信噪比曲线的峰值随着噪声互关联系数和互关联时间的增加而减小.     

具有周期信号调制噪声的线性模型的随机共振

研究了具有周期信号调制噪声的过阻尼线性系统的随机共振现象.当采用非对称的分段噪声 时，可以得到系统响应的一、二阶矩和信噪比的精确表达式.通过对信噪比的分析, 发现了 “真实的"随机共振和传统的随机共振现象，讨论了乘性噪声的非对称性、自相关时间和噪 声之间的相关强度对信噪比的影响. 关键词： 随机共振 信噪比 周期信号调制噪声 线性模型     

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.     

耦合小世界神经网络的随机共振

噪声广泛存在于生物神经系统中,对系统功能具有重要作用.采用神经元二维映射模型构建一个复杂神经网络,由多个小世界子网络构成,研究了Gaussian白噪声诱导的随机共振现象.研究发现,只有合适的噪声强度才能使神经网络对输入刺激信号的频率响应达到峰值.另外,网络结构对系统随机共振特性有重要影响.在固定的耦合强度下,存在一个最优的局部小世界子网络结构,使得整个系统的频率响应最佳.     

Optimal information transmission in nonlinear arrays through suprathreshold stochastic resonance

We examine the optimal threshold distribution in populations of noisy threshold devices. When the noise on each threshold is independent, and sufficiently large, the optimal thresholds are realized by the suprathreshold stochastic resonance effect, in which case all threshold devices are identical. This result has relevance for neural population coding, as such noisy threshold devices model the key dynamics of nerve fibres. It is also relevant to quantization and lossy source coding theory, since the model provides a form of stochastic signal quantization. Furthermore, it is shown that a bifurcation pattern appears in the optimal threshold distribution as the noise intensity increases. Fisher information is used to demonstrate that the optimal threshold distribution remains in the suprathreshold stochastic resonance configuration as the population size approaches infinity.     

Enhanced information transmission with signal dependent noise in an array of LIF neurons

Sensory cells usually transmit information to afferent neurons via chemical synapses, in which the level of noise is dependent on an applied stimulus. Taking into account such dependence, we model a sensory system as an array of LIF neurons with a common signal. We show that information transmission is enhanced by a nonzero level of noise. Moreover, we demonstrate a phenomenon similar to suprathreshold stochastic resonance with additive noise. We remark that many properties of information transmission found for the LIF neurons was predicted by us before with simple binary units [Phys. Rev. E 75, 021121 (2007)]. This confirmation of our predictions allows us to point out identical roots of the phenomena found in the simple threshold systems and more complex LIF neurons.     

Suprathreshold stochastic resonance induced by ion channel fluctuation

In this study, we examine the signal detection ability of an array of neurons with intrinsic channel fluctuation. Numerical simulations show that estimation of the input signal from the output spiking activity of the neuronal array is most accurate if a proper amount of channel noise exists. Theoretical calculation of the mutual and Fisher information confirms the effect of the noise-aided information transfer in the array, or the presence of suprathreshold stochastic resonance. These results indicate that the channel noise, which induces response variability, may play an essential role in population coding.     

Chaos and reverse transitions in stochastic resonance

Stochastic resonance is a phenomenon that a weak signal can be amplified and optimized by the assistance of noise in bistable system. There is still not enough research on the mutual interplay among system, noise and signal. In this paper, we study the role of every parameter in nonlinear transfer and discover chaos phenomenon in stochastic resonance. To measure the influence of chaos, a trajectory decision function was proposed. Based on this function, we found two forms of stochastic resonance, clockwise resonance and counterclockwise resonance.     

声学随机共振实验

在特定的非线性系统中,噪声的存在能够增强信号的响应, 这种现象为随机共振. 本文实验通过观察噪声对听觉阈限的影响,使学生了解声学中的随机共振现象.     

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.     

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.     

Suprathreshold stochastic resonance in multilevel threshold systems

A new form of stochastic resonance (SR) that occurs in multilevel threshold signal detectors is reported. In contrast to classical SR, which extends the dynamic range of threshold detectors to subthreshold signal levels, this new form of SR extends the dynamic range to suprathreshold signal strengths. The effect is most dominant, and can outperform networks based on standard engineering design, when all thresholds adapt to the dc level of the signal. This has an interesting analogy to dc adaptation in neurons. The possible connection between these two effects is discussed.     

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.     

Signal detection for frequency-shift keying via short-time stochastic resonance

A series of short-time stochastic resonance (SR) phenomena, realized in a bistable receiver, can be utilized to detect a train of information represented by signals that adopt frequency-shift keying (FSK). It is demonstrated that the values of noise intensity at resonance regions are close for adjacent periodic signals with an appropriate frequency separation. This establishes the possibility of decoding subthreshold or slightly suprathreshold M-ary FSK signals in bistable receivers. Furthermore, the mechanism of FSK signal detection via short-time SR effects is elucidated in terms of the receiver response speed. This phenomenon provides a possible mechanism for information processing in a bistable device operating in nonstationary noisy environments, where even the inputs appear over a short timescale or have a frequency shift.