松弛型基因随机振子的同步和聚类

松弛型基因随机振子是三类基因振子(光滑振子、松弛振子和随机振子)中的一种.具有相抑制耦合细胞通信的这种类基因振子的同步与聚类是一个有趣且令人关注的问题。这里,数值模拟显示出振子之间的相差分布能够展示出单峰、双峰或多峰分布,但依赖于噪声强度和细胞密度。而且,数值地发现存在细胞数目的一个阈值,当细胞数目超过此阈值时,对于任意的噪声强度相差分布函数的峰值性几乎保持不变。这些结果表明抑制耦合的松弛型随机振子具有不同于普通耦合的光滑或松弛振子的同步与聚类机制。

随机Mathieu系统的Lyapunov指数和稳定性

研究了Ｍａｔｈｉｅｕ系统在随机噪声激励下的主共振响应和稳定性问题．用多尺度法分离了系统的快变项，讨论了系统的阻尼项、随机项等对系统响应的影响．求出了随机Ｍａｔｈｉｅｕ系统的不变测度和最大Ｌｙａ－ｐｕｎｏｖ指数，由最大Ｌｙａｐｕｎｏｖ指数可得系统几乎必然稳定的充分必要条件．

随机多组模型的平稳分布

本文主要利用图论的方法分析具有扩散的随机多组模型的平稳分布。然后,我们利用Lyapunov方法和图论得到了两^保证平稳分布存在的主要定理,其中得到的充分条件具有较少的保守性,反映了平稳分布与随机扰动和拓扑结构密切相关。此外,理论结果被应用到随机耦合振子中。最后, 通过数值模拟说明了本文结果的有效性。

Resonance, Multi-resonance, and Reverse-resonance Induced by Multiplicative Dichotomous Noise

A constant-potential system driven by multiplicative dichotomous noise and subject to an input oscillatory signal is investigated. Two phenomena of stochastic resonance are observed. One is the response as a function of the noise＇s parameters; the other is that as a function of the input signal frequency. A phenomenon of multi-resonance （there are three or four peaks） is found for the response as a function of a parameter of the noise. A phenomenon of reverse-resonance is found, for which the response of the system to the signal can be weakened by the presence of the noise （there is an optimal minimum）. These results help in studies of the systems with multiplicative dichotomous noise, such as the semiconductor, the proteins motor, the chemical reaction, and so on.

Weak-fault diagnosis using state-transition-algorithm-based adaptive stochastic-resonance method

In the early fault period of high-speed train systems, the interested characteristic signals are relatively weak and easily submerged in heavy noise. In order to solve this problem, a state-transition-algorithm (STA)-based adaptive stochastic resonance (SR) method is proposed, which provides an alternative solution to the problem that the traditional SR has fixed parameters or optimizes only a single parameter and ignores the interaction between parameters. To be specific, the frequency-shifted and re-scaling are firstly used to pre-process an actual large signal to meet the requirement of the adiabatic approximate small parameter. And then, the signal-to-noise ratio is used as the optimization target, and the STA-based adaptive SR is used to synchronously optimize the system parameters. Finally, the optimal extraction and frequency recovery of a weak characteristic signal from a broken rotor bar fault are realized. The proposed method is compared with the existing methods by the early broken rotor bar experiments of traction motor. Experiment results show that the proposed method is better than the other methods in extracting weak signals, and the validity of this method is verified.

上帝是如何掷骰子的

通过《用Kendall过程分析随机偶极振子的统计规律》(参看文献 [1] )来揭示如何用“随机过程”对随机现象进行数学摸拟、建立数学模型 ,进行科学推理、演绎及归纳等的分析方法 。

Suppression of Soliton Timing Jitters in Fibers with Random Birefringence by Periodical Polarization Modulation

Periodical polarization modulation scheme is proposed to suppress timing jitters induced by frequency fluctuations between two polarization components of solitons. In periodical polarization modulation scheme, the polarization states of the soliton are modulated to excite equally for suppressing timing jitters induced by two unequal polarization components in the soliton trapping. Moreover, polarization modulation can weaken the effect of random birefringence on the soliton pulses in each relay distance. The numerical result shows that the soliton timing jitters are suppressed by our proposed method.

STOCHASTIC SYNCHRONIZATION OF CIRCADIAN RHYTHMS

Models of circadian genetic oscillators involving interlinked feedback processes in molecular level genetic networks in Drosophila melanogaster and Neurospora crassa are studied, and mechanisms whereby synchronization can arise in an assembly of cells are examined. The individual subcellular circadian oscillatory processes are stochastic in nature due to the small numbers of molecules that are involved, and are subject to large fluctuations. The authors investigate and present the simulations of the stochastic dynamics of ensembles of clock-regulating proteins in different nuclei that communicate via ancillary small molecules, environmental parameters, additive cellular noise, or through diffusive processes. The results show that the emergence of collective oscillations is a macroscopic observable which has its origins in the microscopic coupling between distinct cellular oscillators.

Stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative

The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.

Escape of Brownian particles and stochastic resonance with low-temperature quantum fluctuations

In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/kBT, kB is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.