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     

Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.     

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.     

随机基因选择模型中的延迟效应

研究了噪声驱动的基因选择模型中的延迟效应. 据小延迟方法和随机等价法则得到相应的延迟Fokker-Planck方程, 给出稳态概率分布函数的近似表达式. 分析了在噪声驱动下, 延迟时间对系统稳态性质的影响. 结果表明: 延迟时间可以诱导系统从单稳态向双稳态转化, 发生相变; 在基因选择过程中, 延迟时间有利于从基因群体中选择出某一单倍体基因. 数值模拟结果与理论预测基本符合.     

非线性两能级系统中的Landau-Zener-Coulomb跃迁

非线性跃迁动力学的研究是量子操控中的一个重要课题,在原子分子光物理、量子信息以及固体物理等领域都有着重要的应用.本文研究了具有粒子间相互作用两能级系统中的Landau-Zener-Coulomb跃迁动力学.结果表明,对于能级的斜率正负不同的情况,粒子间相互作用对系统跃迁动力学的影响完全不同.为正时,粒子间相互作用总是抑制能级间的非绝热跃迁,且相互作用强度越大,两能级间的非绝热跃迁越难发生.而为负时,弱相互作用会促进能级间的非绝热跃迁,在强相互作用情况下,跃迁概率会出现振荡.随着相互作用强度的增大,振荡幅度逐渐减小,能级间的非绝热跃迁受到抑制.     

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     

ν↓型三能级原子系统中Raman跃迁增强的Kerr非线性效应

在理论上研究了ν↓型三能级原子系统Raman跃迁中的线性和非线性极化率．研究表明：Raman跃迁中，如果原子完全被抽运到与控制光作用的基态时，将导致介质对探针光的线性极化率为零，而三阶非线性极化率不为零．通过减小原子两基态间的无辐射衰减速率γ12，可以极大地增强交叉Kerr非线性效应．     

类锂离子内壳激发1s22s22S态的电离势和Auger跃迁率

采用鞍点变分方法和鞍点复数转动方法,并考虑相对论修正、质量极化效应,计算了类锂等电子系列(Z=10～20) 1s2s2 2S态的电离势、Auger跃迁率和辐射跃迁率． 同时还计算了QED效应和高阶相对论修正对电离势的贡献．     

分布式光纤中的稳健时间延迟估计方法

在分布式光纤传感系统定位中,传统时延估计算法常由于噪声相关性较强而失效。采用一种削弱相关噪声的改进型广义相关法,并针对系统特点,为进一步改善分布式光纤传感定位的准确度与稳定度,提出了一种先对数据按事件信号进行分帧,再采用卡尔曼滤波器对分帧时延估计结果进行跟踪的时延估计方案。系统仿真实验与实际数据测试结果均表明:提出的时延估计方案能够有效抑制强相关性的噪声,提高时延估计的准确度与稳定度。经大量现场测试,本文的方案能够有效地将时延估计误差稳定地控制在0.2个采样间隔以内,能够满足系统实际定位精度要求。     

时间延迟增强双稳系统的共振抑制

研究了时间延迟对双稳系统激活率的影响.在短时间延迟的情况下,应用最陡下降法导出延迟双稳系统的平均首通时间表达式和相应的与延迟时间有关的激活率表达式.数值计算结果表明,时间延迟可以增强双稳系统的共振抑制.     

The nonequilibrium phase transition and the symmetry revival induced by time delay in an asymmetric bistable system with correlated noises

The nonequilibrium phase transition and the symmetry revival induced by time delay in a bistable system are investigated. The stationary probability distribution function (SPDF) of the bistable system with time delay and correlated noises are calculated by an analytical method and stochastic simulation respectively. The analytical and simulative results indicate that: (1) There is a certain value of λ (λ denotes the strength of correlations between the multiplicative and additive noises) to make the SPDF symmetric under some time delay; however, above or below the given value, the symmetry will be broken; (2) With the monotonic change of λ , the unimodal peak structure of SPDF becomes bimodal at the beginning, then it becomes unimodal again; this means that there is a reentrance phenomenon in the process; (3) There is a critical value of delay time, which makes the lower peak of SPDF equal to the higher one under the critical condition. This means that the symmetry revival phenomenon emerges.     

Effect of time delay on the upper bound of the time derivative of information entropy in a stochastic dynamical system

The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U_B(t) of the time derivative of the information entropy. The results show that there is a critical value of τ (delay time), and U_B(t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, τ can induce a reentrance transition. Delay time τ also causes a reversal behaviour in U_B(t)-λ plot, where λ denotes the degree of the correlation between the two noises.     

时间延迟对基因调节回路中生物记忆影响研究

生物记忆是广泛存在于各种生物子系统的一种重要的效应. 基于一个双反馈的基因调节回路模型, 采用数值模拟的方法研究了局部反馈中存在的时间延迟对生物记忆时间的影响. 结果发现, 小量的延迟能够很大地提高生物记忆时间. 并且, 生物记忆随延迟时间呈线性增加. 这种增强模式与噪声对生物记忆时间的提高完全不同. 延迟和噪声对生物记忆的提高可以进行相互的控制增强, 但不会影响对方的增强模式.     

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

This paper investigates the stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio R_{\rm SNR} is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength \lambda and the delay time \tau on R_{\rm SNR} are respectively discussed. The existence of a peak in the curves of R_{\rm SNR} as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that \lambda and \tau play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing \lambda whereas it is enhanced with the increase of \tau, which is different from the case where the periodic signal is additive.     

Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T _c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T _c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T _c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.      

掺铒光纤中亚稳态粒子振荡和慢光时间延迟关系研究

由于光纤慢光在实际中的应用价值引起广泛关注. 技术手段上利用相干布居振荡效应实现光速可控更具有优势. 本文主要介绍了利用相干布居振荡效应 (CPO) 实现掺铒光纤中的光速减慢传输, 通过改变掺杂浓度、光纤长度、入射信号光及抽运光功率等参量, 具体研究了亚稳态粒子振荡和时间延迟的关系. 研究结果表明: 选择高浓度光纤、增加光纤长度、关闭抽运光源, 选择适当强度的信号光可以有效地增大时间延迟. 关键词： 掺铒光纤 时间延迟 相干布居振荡 慢光     

A class of asymptotic solution for the time delay wind field model of an ocean

A time delay model of a two-layer barotropic ocean with Rayleigh dissipation is built. Using the improved perturba- tion method, an analytic asymptotic solution of a better approximate degree is obtained in the mid-latitude wind field, and the physical meaning of the corresponding solution is also discussed.