色关联乘性和加性色噪声驱动的多稳态系统的稳态特性

研究了色关联乘性和加性色噪声作用下的三稳态系统的稳态问题.首先利用一致有色噪声近似方法,推导出稳态概率密度函数的表达式,然后分析了乘性噪声和加性噪声的强度以及关联性对稳态概率密度函数的影响,研究结果表明:加性噪声强度、加性噪声和乘性噪声的关联强度和关联时间可以诱导系统的非平衡相变.     

Colored Gaussian noises induced stochastic resonance and stability transition for an insect growth system driven by a multiplicative periodic signal

In this paper, we focus on investigating the steady-state shift behaviors and the stochastic resonance phenomenon (SR) for a biological insect population system with a multiplicative periodic signal caused by the terms of the colored multiplicative and additive noises. Our research results imply that the multiplicative noise and the self-correlation of the additive noise can weaken the stability of the biological system and restrain the growth of the insect population, while the additive noise and the self-correlation time of the multiplicative noise can strengthen the stability of the insect system and facilitate the biological population to breed. As regards to the phenomenon of the SR evoked by a multiplicative periodic signal, noise terms and their correlation times, the computed results show that the additive noise intensity M and the self- correlation time τ₁ of the multiplicative noise can both improve the SR effect. Inversely, the multiplicative noise intensity Q and the self-correlation time τ₂ of the additive noise can suppress together the SR phenomenon. Whereas, it should be pointed out that in the SNR-Q and SNR-M plots, the two self-correlation times can both motivate a resonant peak, but not change the peak value of the SNR no matter how the two noise correlation times vary.     

Fluctuations of Single-Mode Laser Driven by Two Different Kinds of Colored Noise

A single-mode laser with coupling between additive and multiplicative noise terms is investigated when the multiplicative noise and the coupling between two noise terms are colored fluctuations with finite correlation times T1 and τ2. Combining the unified colored noise approximation (UCNA) and the functional analysis, the stationary probability distribution (SPD) and the variance of the laser intensity is derived. It is found that the colored nature of multiplicative noise and the coupling strength between two noise terms can affect both the structure and the height of the SPD, while the colored nature of the coupling between two noise terms can only affect the height of the SPD. The multiplicative noise can enhance the intensity fluctuations while the additive noise can reduce the fluctuations in a laser system. Numerical simulations are presented and consistent to the analytical results.     

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.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.     

色噪声对光学双稳态的影响

采用统一色噪声近似构建了由乘法色噪声驱动的纯吸收型光学双稳态状态方程,并分析了色噪声对光学双稳态的影响,将结果与白噪声驱动的光学双稳态进行比较.结果表明:当乘法噪声与加法噪声处在正关联时,增加乘法色噪声的自关联时间r,光学双稳性的区域显著变宽,即磁滞回线面积变大;当乘法噪声与加法噪声处在负关联时,只有乘法噪声较小时,改变乘法色噪声的自关联时间r,光学双稳态才发生改变;当乘法噪声的自相关时间等于零时,本文模型退化为乘法白噪声驱动的光学双稳性状态方程.     

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     

激光相干场成像散斑噪声复合去噪方法

噪声是影响激光相干场高分辨成像系统像质的重要因素,激光相干场成像系统既受背景光加性噪声影响,又受激光乘性散斑噪声影响.为解决激光相干场成像系统受激光乘性散斑噪声和背景光加性噪声叠加引起的成像像质退化效应问题,从噪声抑制角度提高激光相干场系统高分辨成像像质,研究建立了激光散斑乘性噪声和背景光加性噪声对大气下行链路激光回波场信号影响干扰模型,并基于该模型提出了一种基于同态滤波和稀疏基追踪级联复合去噪算法.首先基于同态滤波理论将激光乘性散斑噪声转化为加性噪声,再由高通滤波器滤除散斑噪声,最后采用基追踪稀疏理论方法抑制背景光等加性噪声对像质的影响.研究表明,较现有单一去噪方法,该级联复合去噪方法可一次性消除激光乘性散斑噪声和背景加性噪声两种不同性质的噪声,有效改善了激光相干场成像质量.     

Stochastic resonance in a bias linear system with multiplicative and additive noise

In this paper, the stochastic resonance in a bias linear system subjected multiplicative and additive dichotomous noise is investigated. Using the linear-response theory and the properties of the dichotomous noise, this paper finds the exact expressions for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive noise, and it varies non-monotonously with the intensity and asymmetry of the multiplicative noise as well as the external field frequency. Moreover, the SNR depends on the system bias, the intensity of the cross noise between the multiplicative and additive noise, and the strength and asymmetry of the additive noise.     

Correlated noise-based switches and stochastic resonance in a bistable genetic regulation system

The correlated noise-based switches and stochastic resonance are investigated in a bistable single gene switching system driven by an additive noise (environmental fluctuations), a multiplicative noise (fluctuations of the degradation rate). The correlation between the two noise sources originates from on the lysis-lysogeny pathway system of the λ phage. The steady state probability distribution is obtained by solving the time-independent Fokker-Planck equation, and the effects of noises are analyzed. The effects of noises on the switching time between the two stable states (mean first passage time) is investigated by the numerical simulation. The stochastic resonance phenomenon is analyzed by the power amplification factor. The results show that the multiplicative noise can induce the switching from “on” → “off” of the protein production, while the additive noise and the correlation between the noise sources can induce the inverse switching “off” → “on”. A nonmonotonic behaviour of the average switching time versus the multiplicative noise intensity, for different cross-correlation and additive noise intensities, is observed in the genetic system. There exist optimal values of the additive noise, multiplicative noise and cross-correlation intensities for which the weak signal can be optimal amplified.     

Reentrant transitions in globally coupled active rotators with multiplicative and additive noises

We study the nonequilibrium phenomena in globally coupled active rotators with multiplicative and additive noises. It is shown that at a critical value of the multiplicative noise intensity the system undergoes noise-induced transition from a one-cluster state to a two-cluster state. Additive noise suppresses the effect of the multiplicative noise on the system, increasing the critical value of the multiplicative noise intensity. The system shows a reentrant transition at intermediate additive noise intensity.     

加性噪声对激光一级相变类比的影响

从单模激光场的增益－噪声模型出发,导出了激光场定态强度分布函数,研究了定态分布函数的极值点随加性噪声、乘性噪声和注入信号的变化情况。结果表明,乘性噪声是使激光系统出现一级相变类比的关键因素,注入信号使相变行为减弱,而加性噪声却使得定态分布中极值点的数量和位置出现来回跳跃式变化。     

色关联的色噪声驱动的分段非线性模型的平均首次穿越时间

研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中, 噪声强度和相关时间对平均首次穿越时间的影响. 利用一致有色噪声近似方法和最速下降方法, 推导出系统平均首次穿越时间的表达式. 研究结果表明: 系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构, 即“共振”现象, 峰值会随着加性噪声强度和噪声之间关联强度的增加而减小. 而平均首次穿越时间作为加性噪声的函数呈单调曲线, 说明乘性噪声和加性噪声对平均首次穿越时间的影响不同. 此外, 乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时 对系统平均首次穿越时间的影响是不同的. 关键词： 色噪声 分段非线性系统 平均首次穿越时间     

Stochastic resonance of a periodically driven neuron under non-Gaussian noise

We investigate the first-passage-time statistics of the integrate-fire neuron model driven by a sub-threshold harmonic signal superposed with a non-Gaussian noise. Here, we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term. Such a mechanism generates a power-law distributed noise whose characteristic decay exponent can be finely tuned. We performed numerical simulations to analyze the influence of the noise non-Gaussian character on the stochastic resonance condition. We found that when the noise deviates from Gaussian statistics, the resonance condition occurs at weaker noise intensities, achieving a minimum at a finite value of the distribution function decay exponent. We discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons, as the present result indicates that neurons would require a lower noise level to detect a sub-threshold signal when its statistics departs from Gaussian.     

Steady-state analysis subject to a coloured and a white additive of a bistable system multiplicative noise noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.     

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.     

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     

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.