Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.     

集合种群的延时效应

用简化的延时率函数模型对集合种群的稳定性和平均灭绝时间进行研究.对集合种群的定态概率分布函数和平均首通时间的分析和计算,发现：1)延迟时间增大将使集合种群在斑块中占有率减小;2) 随延迟时间增大,集合种群的灭绝时间将会减小. 关键词： 集合种群 延时效应 灭绝时间     

Two different kinds of time delays in a stochastic system

The steady state properties of a noise-driven bistable system are investigated when there are two different kinds of time delays existed in the deterministic and fluctuating forces respectively. Using the approximation of the probability density approach, the delayed Fokker-Planck equation is obtained. The stationary probability distribution (SPD) and the variance of the system are derived. It is found that the time delay τ in the deterministic force can reduce the fluctuations while the time delay β in the fluctuating force can enhance the fluctuations. Numerical simulations are presented and are in good agreement with the approximate theoretical results.     

不同模式耦合下偏振模色散几率分布的研究

研究了偏振模色散的统计特性,在不同模式耦合条件下,应用蒙特-卡罗方法模拟偏振模色散矢量的几率分布,并对模拟结果进行了函数拟合。发现随着耦合次数增加差分群时延的几率分布从一个类似δ函数分布逐渐过渡到麦克斯韦分布;在一定的耦合下,几率分布可以呈现高斯分布。对偏振模矢量的两个方向余弦进行统计分析,发现随着耦合次数的增加,偏振模矢量两个方向余弦函数的分布从高斯分布和δ函数分布都变为均匀分布。     

Time-Delay Induced Reentrance Phenomenon in?a?Triple-Well Potential System Driven by?Cross-Correlated Noises

The effects of the time delay on the stationary properties of a triple-well potential system driven by the cross-correlated multiplicative and additive noises are investigated. The stationary probability distribution function (SPDF) is obtained by means of a numerical simulation method. The results indicate that: (i) The time delay can induce the reentrance phenomenon with increasing the delay time; (ii) The cross-correlation between the multiplicative and additive noises induces the symmetry breaking of the SPDF.     

Non-Maxwellian probability density function of fibers with lumped polarization mode dispersion elements

We give an analytical expression for the probability density function of the differential group delay for a concatenation of Maxwellian fiber sections and an arbitrary number of lumped elements with constant and isotropically oriented birefringence. When the contribution of the average squared of the constant birefringence elements is a significant fraction of the total, we show that the outage probability can be significantly overestimated if the probability density function of the differential group delay is approximated by a Maxwellian distribution.     

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.     

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.     

Polarization Mode Dispersion Probability Distribution for Arbitrary Mode Coupling

The probability distribution of the differential group delay for arbitrary mode coupling is simulated with Monte-Carlo method. Fitting the simulation results, we obtain probability distribution function for arbitrary mode coupling.     

Experimental investigation of a bistable system in the presence of noise and delay

We experimentally analyze the behavior of a non-Markovian bistable system with noise, using a vertical cavity surface emitting laser with time-delayed optoelectronic feedback. The effects of the delayed feedback are observed in the probability distribution of the residence times of the two orthogonal polarization states, and in the polarization-resolved power spectrum. They agree well with recent theoretical predictions based on a two-state model with transition rates depending on an earlier state of the system. We also observe experimentally and explain theoretically that the residence time probability distribution deviates from exponential decay for residence times close to (and smaller than) the delay time.     

部分时滞诱发Watts-Strogatz小世界神经元网络产生随机多共振

已有研究显示时滞可诱发神经元网络产生随机多共振,但它们主要讨论了神经元间的耦合都存在时滞的情形.然而实际中,有些神经元间的信息传递是瞬时的或时滞很小可以忽略的,即神经元网络中只有部分神经元间的耦合具有时滞,简称部分时滞(若神经元网络内共有l条耦合边,其中有l1条耦合边是具有时滞的,而剩余的耦合边的时滞为零,则我们称这类时滞为部分时滞).本文以Watts-Strogatz小世界神经元网络为研究对象,主要讨论部分时滞对该神经元网络系统响应强度的影响.研究结果指出,系统响应强度随部分时滞的增加呈现多峰的变化态势,即部分时滞可诱发随机多共振现象;而且使系统响应强度达到最优水平的部分时滞的取值区间随随机时滞边概率的增加渐渐变窄,当随机时滞边概率足够大时,系统响应强度只有在时滞位于外界信号周期的整数倍附近才会达到最优.此外,我们还分析了随机连边概率和神经元网络中边的总数对部分时滞诱发的随机多共振现象的影响.结果显示,部分时滞诱发的随机多共振现象对随机连边概率具有一定的鲁棒性,而神经元网络中边的总数对部分时滞诱发的随机多共振的影响则较大.     

Polarization mode dispersion probability distribution for arbitrary distances

The probability distribution of the differential group delay (DGD) at any fiber length is determined by use of a physically reasonable model of the fiber birefringence. We show that if the fiber correlation length is of the same order as or larger than the beat length, the DGD distribution approaches a Maxwellian in roughly 30 fiber correlation lengths, corresponding to a couple of kilometers in realistic cases. We also find that the probability distribution function of the polarization dispersion vector at the output of the fiber depends on the angle between it and the local birefringence vector on the Poincaré sphere, showing that the DGD remains correlated with the orientation of the local birefringence axes over arbitrarily long distances.     

散射介质中多重散射太赫兹脉冲的时域统计特性

对散射介质中多重散射太赫兹脉冲的时域统计特性进行了分析.给出了时间延迟量取不同值时电场的概率分布、散射场强度及其概率分布、散射场实部和虚部的概率分布.由于脉冲的宽带特性及瞬间特性,多重散射场概率统计分布与不同时间延迟量有关,太赫兹脉冲多重散射场的统计特性分布是非平稳过程.     

Stochastic tumor growth system with two different kinds of time delay

The dynamical properties of a noise-driven tumor cell growth system are investigated when there exist two different kinds of time delays, in the deterministic and fluctuating forces, respectively. Using the approximation probability density approach, the delayed Fokker-Planck equation is obtained. The effects of two different time delays on the stationary probability distribution (SPD), the mean value and the mean passage time (MFPT) are discussed. It is found that the time delay τ₁ in the deterministic force can enhance tumor cell number, while the time delay τ₂ in the fluctuating force can induce a decrease in tumor cell numbers. On the other hand, while τ₁ can hold back the extinction of tumor cells, τ₂ can speed up their extinction.     

Time-Delayed Feedback Control in a Single-Mode Laser System

The effects of time-delayed feedback control in a single-mode laser system is investigated. Using the small time delay approximation, the analytic expression of the stationary probability distribution function of the laser field is obtained. The mean, normalized variance and skewness of the steady-state laser intensity are calculated. It is found that the time-delayed feedback control can suppress the intensity fluctuation of the laser system. The numerical simulations are in good agreement with the approximate analytic results.     

Delay-induced intermittent transition of synchronization in neuronal networks with hybrid synapses

We study the dependence of synchronization transitions in scale-free networks of bursting neurons with hybrid synapses on the information transmission delay and the probability of inhibitory synapses. It is shown that, irrespective of the probability of inhibitory synapses, the delay always plays a subtle role during synchronization transition of the scale-free neuronal networks. In particular, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. In addition, it is found that, for smaller and larger probability of inhibitory synapses, intermittent synchronization transition is relatively profound, while for the moderate probability of inhibitory synapses, synchronization transition seems less profound. More interestingly, it is found that as the probability of inhibitory synapses is large, regions of synchronization are upscattering.     

Effect of time delay in FitzHugh-Nagumo neural model with correlations between multiplicative and additive noises

We study the effect of time delay in the FitzHugh-Nagumo neural model with correlations between multiplicative and additive noise terms. Based on the corresponding Fokker-Planck equation, the explicit expressions of the stationary probability distribution function (SPDF), the mean first passage time (MFPT) and the signal-to-noise ratio (SNR) are obtained, respectively. Research results show that: (i) the system undergoes a succession of two phase transitions (i.e., the reentrance phenomenon) as the noise correlation parameter is increased and a (single) phase transition as the time delay is increased. (ii) The MFPT as a function of the multiplicative noise intensity exhibits a maximum. This maximum for MFPT identifies the noise enhanced stability (NES) effect, the noise correlation parameter intensifies the NES effect while the time delay, and the additive noise intensity weakens it. (iii) The existence of a maximum in the SNR as a function of the multiplicative noise intensity is the identifying characteristic of the stochastic resonance (SR) phenomenon, the noise correlation parameter enhances the SR while the time delay, and the additive noise intensity weaken it.     

The effect of stochastic accelerating and delay probability with the velocity and the gap between vehicles on traffic flow

This paper proposes a new combined cellular automaton (CA) model considering the driver behavior of stochastic acceleration and delay with the velocity of the preceding vehicle and the gap between the successive vehicles based on the WWH model and the noise-first NaSch model. It introduces the delay probability varying with the gap, adds the anticipation headway and increases the acceleration with a certain probability. Through these simulations, not only can the metastable state and start--stop wave be obtained but also the synchronized flow which the wide moving jam results in. Moreover, the effect of stochastic acceleration and delay on traffic flow is discussed by analyzing the correlation of traffic data. This indicates that synchronized flow easily emerges in the critical area between free flow and synchronized flow when acceleration and delay are synchronized or their probability is close to 0.5.     

An improved cellular automaton traffic model considering gap-dependent delay probability

In this paper, the delay probability of the original Nagel and Schreckenberg model is modified to simulate one-lane traffic flow. The delay probability of a vehicle depends on its corresponding gap. According to simulation results, it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probability. In comparison with the NS model, one notes that the fundamental diagram of the new model is more consistent with the results measured in the real traffic, and the velocity distributions of the new model are relatively reasonable.