色噪声对光学双稳态的影响（英文）

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τ,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τ,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.     

色关联噪声驱动的非对称双稳系统中平均首次穿越时间的研究

研究了由色关联的乘性白噪声和加性白噪声驱动的非对称双稳系统中，色关联及非对称性对平均首次穿越时间的影响.数值结果表明乘性噪声强度α和加性噪声强度D及互相关时间τ对首次穿越时间T的影响是一致的，加性和乘性噪声间的互关联强度λ及势阱的非对称性r对T的影响是一致的.τ的增加能提高粒子的逃逸率，λ的增加则减小逃逸率.     

双色噪声驱动光学双稳系统的弛豫时间研究

研究乘性及加性噪声的自关联时间τ₁和τ₂,交叉关联时间τ对光学双稳系统的弛豫时间的影响.弛豫时间T由Mei等所采用的方法得到. 经数值计算, 结果表明: 两噪声间交叉关联时间τ及乘性噪声的自关联时间τ₁延缓系统涨落的消退(T随τ及τ₁的增大而增大);T随加性噪声的自关联时间τ 关键词： 关联噪声 弛豫时间 光学双稳系统     

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     

色噪声驱动的非对称双稳系统的平均首次穿越时间

研究了由关联乘性色噪声及加性白噪声驱动的非对称双稳系统中势阱的非对称性及噪声对系统两个方向平均首次穿越时间的影响. 首先利用一致有色噪声近似推导了系统的稳态概率密度的表达式，根据最速下降法推导了平均首次穿越时间的表达式. 数值结果表明：势阱的非对称性对两个方向的平均首次穿越时间的影响是不同的；由于噪声的关联性，即使对于关联乘性色噪声及加性白噪声驱动的对称双稳系统，两个方向的平均首次穿越时间也不再相等；在lnT₊-r和lnT_{-关键词： 平均首次穿越时间 非对称双稳系统 乘性色噪声 加性白噪声}     

关联噪声驱动系统的一阶数值模拟算法

在某些条件下共同驱动随机系统的乘法噪声和加法噪声可以相互关联,相关噪声驱动的随机微分系统具有独特的性质,而数值模拟是研究这类系统一种强有力的方法。研究相关噪声驱动系统的数值模拟算法,分别就白噪声情形和色噪声情形作了讨论,得到了一种一阶数值模拟算法,并与已有文献的解析结果进行了对比。     

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.     

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     

双色噪声驱动非对称双稳系统平均第一穿越时间研究

利用统一色噪声近似理论,研究乘性色噪声和加性色噪声驱动的非对称双稳系统中,势阱的非对称性和噪声对系统两个方向的平均第一穿越时间T₊（x_s1→x_s2）和T_-（x_s2→x_s1）的影响（x_s1和x_s2是双稳系统的两个稳定点）.数值结果表明：T₊（x_s1→x_s2）随乘性噪声的自关联时间τ₁以及加性噪声的自关联时间τ₂的增大而减小.T_-（x_s2→x_s1）随乘性噪声的自关联时间τ₁以及加性噪声的自关联时间τ₂的增大而增大.在曲线（T₊（x_s1→x_s2）,λ）和（T_-（x_s2→x_s1）,λ）上都存在单峰.T₊（x_s1→x_s2）随非对称系数r的增大而增大,T_-（x_s2→x_s1）随非对称系数r的增大而减小. 关键词： 统一色噪声近似 平均第一穿越时间 加性色噪声 乘性色噪声     

色交叉关联噪声作用下癌细胞增长系统的平均首通时间

研究了受色交叉关联噪声驱动的癌细胞增长系统的平均首通时间.根据Novikov定理和Fox方法得到了相应的近似Fokker-Planck方程,给出了稳态概率密度函数的表达式.运用最快下降法,得到了平均首通时间的解析式.数值结果表明:两噪声之间负关联时,平均首通时间是加性噪声强度和乘性噪声强度的减函数,是噪声关联时间的增函数;两噪声之间正关联时,平均首通时间与加性噪声强度之间的单调关系与穿越方向有关,是乘性噪声强度的非单调函数,是噪声关联时间的减函数.     

Correlation function of an optical bistable system with cross-correlated additive white noise and multiplicative colored noise

Considering an optical bistable system with cross-correlated additive white noise and multiplicative colored noise, we study the effects of correlation between the noises on the correlation function C（s） using the unified colored noise approximation and the Stratonovich deeoupling ansatz formalism. The effects of the self-correlation time τ of the multiplicative colored noise and the correlation intensity λ between the two noises are studied with numerical calculation. It is found that C（s） increases with the increase of the self-correlation timeτ, but decreases with the increase of the correlation intensity λ. At large value of τ, there is almost no change for C（s） when τ changes.     

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.     

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 Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

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.     

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     

Multiplicative non-Gaussian noise and additive Gaussian white noise induced transition in a piecewise nonlinear model

We study the transition problems in a piecewise nonlinear model induced by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Firstly, applying the path integral approach, the unified colored noise approximation, the analytical expression of the steady-state probability density function (SPD) is derived. Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise. From numerical computations we obtain some new nonlinear phenomena: the transition can be induced by the cross-correlation strength between noises, the non-Gaussian noise intensity and the Gaussian noise intensity as well as the non-Gaussian noise deviation parameter. This indicates that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. Moreover, we also find the correlation time of the non-Gaussian noise can not induce the transition.     

白交叉关联色噪声驱动的线性振子的扩散

研究了由白交叉相关的两色噪声所驱动的线性振子的扩散,其中一个噪声受偏置的周期信号所调制.揭示了乘性色噪声的自关联时间τ1和加性色噪声的自关联时间τ2对d-Q,d-D及d-Ω曲线的影响,其中d,Q,D和Ω分别为振子的扩散系数、受信号调制的噪声强度、未受调制的噪声强度和信号的频率.发现d-Q和d-D曲线均存在一个极小值,而d-Ω曲线则在Ω=～Ω处呈现极大值,～Ω为振子频率.推导了使扩散系数d=0的条件.