Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise,we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s)is derived by means of the projection operator method.The effects of the self- correlation timeτ_1 of the additive colored noise,τ_2 of the multiplicative colored noise,and the effect of the cross-correlation timeτ_0 between the two noises on C(s)are discussed by numerical calculation.For the case of positive correlation(λ> 0),it is found that when a_0 > 0 the normalized intensity correlation function C(s)increases with the increase of To orτ_2,and with value ofτ_0 orτ_2 becoming larger,C(s) comes to saturation.With increasing the self-correlation timeτ_1 of the additive noise,a minimum and a maximum will appear on curve of C(s)as a_0 > 0.If a_0 < 0,C(s)decreases with the increase ofτ_0,τ_1, andτ_2.     

Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.     

Stochastic resonance in an optical bistable system subjected to cross-correlated additive white noise and multiplicative colored noise

The stochastic resonance (SR) of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR). Results show that cross-correlation intensity λ enforces the SR of the system. The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ (τ is the self-correlation time of the multiplicative colored noise). We find the SR phenomenon in the SNR-D and SNR-Q curves (D and Q are the intensities of the additive and multiplicative noises, respectively), but not in the SNR-λ curves.     

Study of the normalized intensity correlation function of a single-mode laser system with colored cross-correlated noises

A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation timeτand the cross-correlation intensityλbetween noises on the normalized intensity correlation function C(s). It is found that ifλ> 0 (λ< 0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation timeτ, and at large value ofτ, the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum whenλis larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 whenλbecomes smaller and smaller.     

Intensity Correlation Function and Associated Relaxation Time of a Saturation Laser Model with Correlated Noises

We investigate the intensity correlation function C（s） and its associated relaxation time Tc for a saturation model of single-mode laser with correlated noises. The expressions of O（s） and Tc are derived by means of the projection operator method, and effects of correlations between an additive noise and a multiplicative noise are discussed by numerical calculation. Based on the calculated results, it is found that the correlation strength A between the additive noise and the multiplicative noise can enhance the fluctuation decay of the laser intensity.     

Intensity Correlation Function of a Single-Mode Laser Driven by Two Colored Noises with Colored Cross-Correlation

By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. Moreover, we find that there is a minimum Tmin in the curve of the intensity correlation time versus the pump noise intensity, and the depth and position of Train strongly depend on the quantum noise self-correlation time T2 and cross-correlation time T3.     

Stochastic resonance for a metapopulation system driven by multiplicative and additive colored noises

We investigate the stochastic resonance(SR) phenomenon induced by the periodic signal in a metapopulation system with colored noises. The analytical expression of signal-to-noise is derived in the adiabatic limit. By numerical calculation, the effects of the addictive noise intensity, the multiplicative noise intensity and two noise self-correlation times on SNR are respectively discussed. It shows that:(i) in the case that the addictive noise intensity M takes a small value, a SR phenomenon for the curve of SNR appears; however, when M takes a large value, SNR turns into a monotonic function on the multiplicative noise intensity Q.(ii) The resonance peaks in the plots of the multiplicative noise intensity Q versus its self-correlation time τ1 and the addictive noise intensity M versus its self-correlation time τ2 translate in parallel. Meanwhile, a parallel translation also appears in the plots of τ1 versus Q and τ2 versus M.(iii) The interactive effects between self-correlation times τ1 and τ2 are opposite.     

Effects of cross-correlated noises on the intensity fluctuation of the single-mode laser system

A single-mode laser model with cross-correlated additive and multiplicative noise terms is considered, and the effects of correlation between noises on the relaxation time and the intensity correlation function are studied. Using the projection operator method and taking into account the effects of the memory kernels of the intensity correlation function, the analytic expressions for the relaxation time and the correlation function are derived. Based on numerical computations, it is found that the self-correlation time and the cross-correlation time have the same effects on the single-mode laser system.     

Effects of cross-correlated noises on the intensity fluctuation of the single-mode laser system

A single-mode laser model with cross-correlated additive and multiplicative noise terms is considered, and the effects of correlation between noises on the relaxation time and the intensity correlation function are studied. Using the projection operator method and taking into account the effects of the memory kernels of the intensity correlation function, the analytic expressions for the relaxation time and the correlation function are derived. Based on numerical computations, it is found that the self-correlation time and the cross-correlation time have the same effects on the single-mode laser system.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

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     

偏置信号调制下噪声关联的周期调制对单模激光随机共振的影响

在噪声受偏置信号调制的情况下，讨论色噪声之间的关联受时间周期调制所驱动的单模激光系统中的随机共振.用线性化近似的方法计算了输出信噪比.具体讨论输出信噪比随噪声自关联时间、噪声强度和偏置信号的变化关系.发现输出信噪比随抽运噪声强度和自关联时间的变化出现随机共振，而偏置信号会降低随机共振的峰值.实际应用中应控制优选偏置信号强度. 关键词： 偏置信号 色噪声 时间周期调制 噪声间关联程度     

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     

Influence of low intensity noise on assemblies of diffusively coupled chaotic cells

The effect of time-correlated and white Gaussian noises of low intensity on one-dimensional arrays consisting of diffusively coupled chaotic cells is analyzed. An improvement or worsening of the synchronization between cells of the array driven by low-intensity colored noise is observed for a resonant interval of time correlation values. A comparison between colored and white noise and additive and multiplicative contribution has been carried out investigating the nonlinear cooperative effects of noise strength, correlation time, and coupling strength to control spatiotemporal chaos in coupled arrays of chaotic cells. The possibility to distinguish highly correlated areas of a diffusively coupled network of cells by using low-intensity time correlated noise is discussed. (c) 2001 American Institute of Physics.     

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.     

色交叉关联噪声作用下集合种群的稳定性和平均灭绝时间

在Levins模型的基础上研究了色交叉关联噪声对集合种群稳定性的影响, 应用Fokker-Plank方程得到了系统的稳态概率密度函数, 运用最快下降法得到了平均灭绝时间的解析式. 结果表明: 两噪声色关联时, 加性噪声强度和乘性噪声强度均弱化集合种群的稳定性; 噪声关联强度强化集合种群的稳定性. 两噪声之间负关联时, 平均灭绝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, 平均灭绝时间是加性噪声强度和噪声关联时间乘性噪声强度的减函数, 是乘性噪声强度的非单调函数. 关键词： 集合种群 色交叉关联噪声 稳定性 平均灭绝时间     

Study of the normalized intensity correlation function of a single-mode laser system with colored cross-correlated noises

A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time τ and the cross-correlation intensity λ between noises on the normalized intensity correlation function C(s). It is found that if λ＞ 0 (λ＜ 0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time τ, and at large value of τ, the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when λ is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when λ becomes smaller and smaller.