Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C（τ） and the associated relaxation time T（C） in the case of a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.     

Effects of correlations between the real and imaginary parts of quantum noise on intensity fluctuation for a saturation laser model

This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function ${C(\tau)}$ and the associated relaxation time ${T({C})}$ in the case of a stable locked phase resulting from the cross-correlation ${\lambda_q}$ between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.     

Simulation study of the two-time intensity correlation function of a two-mode laser system with both pump and quantum noises

This paper investigates the two-time intensity correlation function of a two-mode ring laser system subjected to both pump and quantum noises by stochastic simulation. It finds that the decay rate of the intensity correlation function of one mode gets faster with decreasing values of relevant parameters, i.e., the coupling constant ξ, the cross-correlation coefficient λ , the difference of the pump parameters Δa and the pump parameter a₁; however, its variations get complex in the other mode when relevant parameters are changed. The investigating results also show that the effects of the mode competition on intensity correlation function are obvious.     

Effects of time-delay in stationary properties of a logistic growth model with correlated noises

A time-delayed tumor cell growth model with correlated noises is investigated. In the condition of small delay time, the stationary probability distribution is derived and the stationary mean value (〈x〉_st) and normalized varianceλ₂ of the tumor cell population and state transition rate (κ) between two steady states are numerically calculated. The results indicate that: (i) The delay time (τ) enhances the coherence resonance in 〈x〉_st as a function of the multiplicative noise intensity (D) and increases 〈x〉_st as a function of the additive noise intensity (α), i.e., τ enhances fluctuation of the system, however, the strength (λ) of correlations between multiplicative and additive noise plays a contrary role to τ on these; (ii) τ enhances the coherence resonance in κ as a function of D and increases κ as a function of α, i.e., τ speeds up the rate of state transition, however, λ also plays a contrary role to τ on these.     

含关联噪声与时滞项的非对称双稳系统的随机共振

研究了基于关联噪声的带时滞项的非对称双稳系统的随机共振，在小时滞量及绝热近似理论下得到了信噪比的精确解析表达式，表明由于时滞量的存在系统出现了随机共振.讨论了系统的时滞量、噪声相关系数及系统的非对称性对系统的信噪比的影响.     

噪声相互关联时间对Logistic系统亚稳态稳定性的影响

研究了噪声交叉关联时间对Logistic 系统亚稳态稳定性的影响.利用最陡下降法导出了系统亚稳态到稳态的平均第一通过时间的表达式. 数值计算结果表明:内噪声、外噪声、 内外噪声的相互关联时间削弱了亚稳态的稳定性,而内外噪声的关联增加了亚稳态的稳定性.     

关联白噪声驱动的具有时间延迟的Logistic系统

关联白噪声驱动的具有时间延迟的Logistic系统可更真实的反映肿瘤细胞的增长问题,本文通过小时间延迟近似方法对由关联白噪声驱动的具有时间延迟的Logistic系统进行了研究,得到了系统的稳态概率密度,并进一步分析了加性和乘性噪声强度,噪声关联时间和时间延迟对稳态概率密度的影响以及噪声诱导的非平衡相变现象. 关键词： Logistic系统 关联白噪声 时间延迟 非平衡相变     

高斯初始能量分布下自由电子激光饱和状态的统计理论求解

基于高增益自由电子激光饱和状态的统计物理方法,在不同的电子束相空间初始分布下对原有理论进行了发展和推广,借助于多重数值积分技术解决了粒子束一般动量初始分布带来的计算困难,并以更接近实际的高斯动量分布为例进行计算。作为对比验证编写高斯初始动量分布下的直接数值模拟程序,将高斯初始分布同"水袋"两种初始分布的"暖电子束"入射情形下自由电子激光达到饱和时系统的光强、聚束因子和粒子相空间分布均进行相应计算和比较。结果表明:数值模拟和统计计算结果相一致;在目前选取的参数范围内,两种初始分布的相应结果差异并不显著。     

延时对色关联噪声诱导的逻辑生长过程的影响

应用小延时近似方法,研究了色关联噪声诱导的延时逻辑生长过程,得到了肿瘤细胞数的稳态概率分布P_st(x)的近似解析表达式,发现延时τ的变化可以使P_st(x)发生由多极值结构向单极值结构的转换,延时τ还可以使随机系统的平均值〈x〉、二阶矩〈x²〉、归一化涨落V_ar的极值位置和极值大小发生改变. 关键词： 逻辑生长过程 延时 关联色噪声 统计性质     

色关联噪声对林木Logistic生长模型的影响

在林木生长Logistic模型中, 引入加性和乘性关联色噪声, 运用统一色噪声近似、刘维方程以及诺维科夫原理, 推导了近似福克-普朗克方程, 分析了相关参数对稳态概率分布函数的影响. 结果表明: 改变乘性色噪声强度D和加性色噪声强度Q均能导致稳态概率分布曲线峰值高度的改变以及峰位置的移动, 对概率密度分布呈现出漂移作用. 但是在D和Q增大的过程中, 稳态概率分布曲线峰位置的移动方向是不同的: D增大时, 峰的位置向左移动; Q增大时, 峰的位置向右移动. 另外, 当λ >0时, 随着|λ|的增大, 稳态概率分布函数峰的位置向右移动, 且峰值的高度变大; 而λ<0时, 随着|λ|的增大, 稳态概率分布函数峰值的高度也变大, 而峰的位置却向左移动. 关键词： 林木生长 Logistic模型 色噪声 稳态概率分布     

Noise-induced dynamics in a delayed bistable system with correlated noises

The resonance behaviors, such as coherence resonance and stochastic resonance, are studied in a delayed bistable system subject to correlated noises and a weak harmonic excitation. For weak noise intensities and small feedback gains, the analytic expressions of output spectrum and linear spectrum amplification are derived based on the theory proposed by Tsimring [14] [L.S. Tsimring, A. Pikovsky, Noise-induced dynamics in bistable systems with delay, Phys. Rev. Lett. 87 (2001) 250602]. The results show that the peak in the output spectrum at the frequency corresponding to the time delay attains the maximum for an intermediate amount of noise intensity and the coherence resonance appears. The correlation between noises can induce the suppression and the stochastic resonance in the curve of spectrum amplification, which is absent for the case of uncorrelated additive and multiplicative noises. Moreover, the system also exhibits the frequency stochastic resonance.     

Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time (MFPT) and the spectral power amplification (SPA) are obtained, respectively. Based on the numerical computations, it is found that: (i) The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises (λ>0), this maximum for MFPT shows the characteristic of the entropic noise induced stability (ENIS) effect. The intensity λ of correlations between two noises can enhance the ENIS effect. (ii) The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.     

The effects of observational correlated noises on multifractal detrended fluctuation analysis

We have numerically investigated the effects that observational correlated noises have on the generalized Hurst exponents, h(q)$h\left(q\right)$, estimated by using the multifractal generalization of detrended fluctuation analysis (MF-DFA). More precisely, artificially generated stochastic binomial multifractals with increased amount of colored noises were analyzed via MF-DFA. It has been recently shown that for moderate additions of white noise, the generalized Hurst exponents are significantly underestimated for q<2$q<2$ and they are nearly unchanged for q≥2$q\ge 2$ [J. Ludescher, M.I. Bogachev, J.W. Kantelhardt, A.Y. Schumann, A. Bunde, On spurious and corrupted multifractality: the effects of additive noise, short- term memory and periodic trends, Physica A 390 (2011) 2480–2490]. In this paper, we have found that h(q)$h\left(q\right)$ with q≥2$q\ge 2$ are also affected when correlated noises are considered. This is due to the fact that the spurious correlations influence the scaling behaviors associated to large fluctuations. The results obtained are significant for practical situations, where noises with different correlations are inherently present.     

偏置信号调制下色关联噪声驱动的单模激光的光强相对涨落

采用线性化近似，计算了由具有色关联的受偏置信号调制的色泵噪声和色量子噪声驱动 的单模激光增益模型的光强相对涨落，发现相对涨落随噪声强度的变化曲线中存在极小值，分析了偏置信号的强度、周期信号频率、噪声间的互关联强度和互关联时间对曲线的影响； 对单模激光增益模型在偏置信号调制和直接信号调制两种方式下的输出光强相对涨落进行了比较，发现光强涨落与偏置信号的强度密切相关. 关键词： 偏置信号调制 光强相对涨落 线性化近似     

多频染料激光器的相关调谐原理

本文将染料激光系统模式耦合理论应用于三频或多频运转的染料激光器,得到了用“增益-损耗比”和振荡频率所含模数等参量表示的振荡条件关系式,讨论了三频染料激光的振荡状态图及其相关调谐问题.     

Steady-State Analysis of a Two-Mode Laser System with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imag- inary parts of quantum noise is considered. The Fokker-Planek equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that： （i） The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; （ii） The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; （iii） The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.     

Missing ordinal patterns in correlated noises

Recent research aiming at the distinction between deterministic or stochastic behavior in observational time series has looked into the properties of the “ordinal patterns” [C. Bandt, B. Pompe, Phys. Rev. Lett. 88 (2002) 174102]. In particular, new insight has been obtained considering the emergence of the so-called “forbidden ordinal patterns” [J.M. Amigó, S. Zambrano, M.A. F Sanjuán, Europhys. Lett. 79 (2007) 50001]. It was shown that deterministic one-dimensional maps always have forbidden ordinal patterns, in contrast with time series generated by an unconstrained stochastic process in which all the patterns appear with probability one. Techniques based on the comparison of this property in an observational time series and in white Gaussian noise were implemented. However, the comparison with correlated stochastic processes was not considered. In this paper we used the concept of “missing ordinal patterns” to study their decay rate as a function of the time series length in three stochastic processes with different degrees of correlation: fractional Brownian motion, fractional Gaussian noise and, noises with f^−k power spectrum. We show that the decay rate of “missing ordinal patterns” in these processes depend on their correlation structures. We finally discuss the implications of the present results for the use of these properties as a tool for distinguishing deterministic from stochastic processes.     

Moments of the intensity of a single-mode laser driven by coloured pump noises with a cross-correlation between the real and imaginary parts of the quantum noise

By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ_q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity 〈I〉 and variance λ_2 (0) for both below and above the threshold operation, and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ_q makes the 〈I 〉－τ curves exhibit a "re-entrant phase transition". Whether the laser is above or below the threshold, the whole 〈I 〉－τ curve moves down as λ_q increases; however, when λ_q=1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ_2(0)－p′ curve being suppressed (here p′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ_2 (0)－p′ curve as a function of λ_q is similar to that of the 〈I 〉－τ curve against λ_q: that is, whether the laser is above or below the threshold, the λ_2 (0)－p′ curve moves up as λ_q increases; however, when λ_q=1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.τ     

关联白噪声对抗肿瘤体系免疫效果的影响

在免疫监视的Logistic肿瘤生长动力学模型中引入关联的乘性白噪声,并考虑抗肿瘤体系的免疫系统激活阈值存在差异,对上述动力学生长方程进行数值仿真计算.发现噪声关联强度能够调节抗肿瘤体系个体的免疫效果,但调节的结果存在差异;噪声关联强度λ的取值存在一个最佳区间,在该区间内更多的抗肿瘤体系个体能实现最大免疫效果. 关键词： Logistic生长模型 随机涨落 肿瘤 免疫     

Dynamical properties of a logistic growth model with cross-correlated noises

A logistic growth model driven by additive and multiplicative noises which are correlated with each other is investigated. Using the Novikov theorem and the projection operator method, we obtain the analytic expressions of the stationary probability distribution p_st(x), the relaxation time T_c, and the normalized correlation function C(s) of this system. The computational results show that the relaxation time T_c increases as the cross-correlated time τ increases, but decreases while the cross-correlated strength λ increases. The relationship between the relaxation time C(s) and the decay time s is given. Correlation time τ and correlation strength λ play an opposite role on dynamic properties in this logistic growth model.