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1.
Steady-state analysis subject to a coloured and a white additive of a bistable system multiplicative noise noise with coloured cross-correlated noises 总被引:1,自引:0,他引:1 下载免费PDF全文
The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R(R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise), and performing the numerical computations, we find the following points: (1) For the case of R 〉 1, A (the intensity of correlation between additive and multiplicative noises), T1 and T2 can induce the stationary probability distribution (SPD) transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; (2) a can also induce the SPD transition from bimodal to unimodal in structure; (3) the bimodal structure of the SPD exhibits a symmetrical structure as D increases. 相似文献
2.
Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises 下载免费PDF全文
By adding frequency modulated signals to the intensity equation of
gain--noise model of the single-mode laser driven by two coloured
noises which are correlated, this paper uses the linear
approximation method to calculate the power spectrum and
signal-to-noise ratio (SNR) of the laser intensity. The results show
that the SNR appears typical stochastic resonance with the variation
of intensity of the pump noise and quantum noise. As the amplitude
of a modulated signal has effects on the SNR, it shows suppression,
monotone increasing, stochastic resonance, and multiple stochastic
resonance with the variation of the frequency of a carrier signal
and modulated signal. 相似文献
3.
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. 相似文献
4.
The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises.The approximate Fokker-Planck equation is derived based on the Novikov theorem and the Fox approach.By applying the two-state theory,the expression of the signal-to-noise ratio is obtained in the adiabatic limit.The effects of the noise parameters on signal-to-ratio are discussed.It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases. 相似文献
5.
Stochastic resonance driven by time-modulated correlated coloured noise sources in a single-mode laser 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper investigates the phenomenon of stochastic resonance in a
single-mode laser driven by time-modulated correlated coloured noise
sources. The power spectrum and signal-to-noise ratio R of the
laser intensity are calculated by the linear approximation. The
effects caused by noise self-correlation time τ1, τ2
and cross-correlated time τ3 for stochastic resonance
are analysed in two ways: τ1, τ2 and τ3 are
taken to be the independent variables and the parameters
respectively. The effects of the gain coefficient Γ and loss
coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema
in the curve of R versus K is reduced with the increase of the
gain coefficient Γ. 相似文献
6.
Output power spectrum of a single-mode laser driven by coloured pump and quantum noises with coloured correlation 下载免费PDF全文
By using the linear approximation method, the output power spectrum is calculated for a single-mode laser driven by coloured pump and quantum noises with coloured correlation. We have observed that the configuration of the output power spectrum is complicated: that is, it can be of single peak, two peaks or three peaks. The configurations of the power spectrum can be transformed from one into another by changing the cross-correlation time, the cross-correlation coefficient between the two noises, and pump noise intensity. 相似文献
7.
Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times 总被引:2,自引:0,他引:2 下载免费PDF全文
We study a system for a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation. The analytical expression of the stationary intensity distribution (SID) for the laser is derived in the case of three different correlation times. The influences of each stochastic parameter on the SID are discussed, the effects of the noise "colour" and the cross-correlation of noises on the mean intensity , the variance, λ_2(0), and the skewness,λ_3(0) of the single-mode laser are investigated. We find that there are colourful phase transitions for the SID above a threshold, and re-entrant transitions induced by the "colour" of the additive noises. Further research of the curves of -τ_i, λ_2(0)-τ_i, and λ_3(0)-τ_i (i=1,2,3) (where τ_i is the correlation time) shows that the output intensity not only increases with the additive noise correlation time τ_2 and the cross-correlation time τ_3, but also the quality of the output of laser beams is optimized. 相似文献
8.
The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper.According to the Fokker-Planck equation in the unified colored-noise approximation,we analyse the stationary probability distribution and the mean first-passage time of this model.By numerical analysis,the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density.The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model. 相似文献
9.
10.
Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises 下载免费PDF全文
It is shown how the cross-correlation time and strength of coloured cross-correlated white noises can set an upper bound for the time derivative of entropy in a nonequilibrium system. The value of upper bound can be calculated directly based on the Schwartz inequality principle and the Fokker--Planck equation of the dynamical system driven by coloured cross-correlated white noises. The present calculations can be used to interpret the interplay of the dissipative constant and cross-correlation
time and strength of coloured cross-correlated white noises on the upper bound. 相似文献
11.
Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator 下载免费PDF全文
The diffusion in a harmonic oscillator driven by coloured noises
$\xi(t)$ and $\eta(t)$ with coloured cross-correlation in which
one of the noises is modulated by a biased periodic signal is
investigated. The exact expression of diffusion coefficient d as a
function of noise parameter, signal parameter, and oscillator
frequency is derived. The findings in this paper are as follows. 1)
The curves of d versus noise intensity D and d versus noises
cross-correlation time $\tau_3$ exist as two different phases. The
transition between the two phases arises from the change of the
cross-correlation coefficient $\lambda$ of the two
Ornstein--Uhlenbeck (O-U) noises. 2) Changing the value of $\tau_3$, the curves of d versus Q, the intensity of colored noise
that is modulated by the signal, can transform from a phase having a
minimum to a monotonic phase. 3) Changing the value of signal
amplitude A, d versus Q curves can transform from a phase
having a minimum to a monotonic phase. The above-mentioned results
demonstrate that a like noise-induced transition appears in the
model. 相似文献
12.
Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation 下载免费PDF全文
This paper shows the Fokker--Planck equation of a dynamical system
driven by coloured cross-correlated white noises in the absence and
presence of a small external force. Based on the Fokker--Planck
equation and the definition of Shannon's information entropy, the
time dependence of entropy flux and entropy production can be
calculated. The present results can be used to explain the extremal
behaviour of time dependence of entropy flux and entropy production
in view of the dissipative parameter γ of the system, coloured
cross-correlation time \tau and coloured cross-correlation strength
\la. 相似文献
13.
In this paper, we studied the effect of Gaussian coloured noise on
the formation and instability of spiral waves described by one class
of modified FitzHugh--Nagumo equation. It was found that Gaussian
coloured noise plays a constructive role in the formation,
transition and instability of spiral wave. Too weak or too strong
noise may act against the formation of spiral waves. At a certain
noise level, spiral wave is maintained in a medium, in which spiral
wave cannot be observed in the absence of the noise. It is difficult
to make a stable spiral wave into unstable state by Gaussian
coloured noise, unless the noise level is very high. The parameter
regions of Gaussian coloured noise for spiral forming and spiral
instability were given and discussed with numerical simulations. 相似文献
14.
15.
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 总被引:1,自引:0,他引:1 下载免费PDF全文
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 相似文献
16.
本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加. 相似文献
17.
18.
Intensity correlation time of a single-mode laser driven by two coloured noises with coloured cross-correlation with direct signal modulation 下载免费PDF全文
In this paper, the intensity correlation time T is studied for the gain-noise model of a single-mode laser driven by coloured pump noise and coloured quantum noise with coloured cross-correlation with a direct signal modulation. By using the linear approximation method, it is found that when the pump noise is modulated directly by a signal, the effects of the cross-correlation between the pump noise and the quantum noise will disappear. In addition, there exists a maximum (i.e. resonance) in the curve of the intensity correlation time $T$ versus the pump noise self-correlation time \tau1. Furthermore, when \tau1\le\tau2, the intensity correlation time T increases monotonically with the increase of $D$ and decreases monotonically with the increase of Q, but when \tau1>\tau2, the intensity correlation time T increases monotonically with the increase of Q and decreases monotonically with the increase of D. 相似文献
19.
The linear relaxation time (LRT) associated with steady-state correlation functions is studied for Langevin equations with non-Gaussian noises: dichotomous Markov noise and Poissonian white shot noise. Exact results for arbitrary models are obtained and compared with results for Gaussian noises. Some general features of LRTs are discussed. The concept of dynamic effective diffusion is introduced and the existence of an optimal effective Fokker-Planck approximation is discussed. Explicit examples for prototype models are presented and briefly compared with the analogs for Gaussian noises. 相似文献