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1.
Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation
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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
2.
In this paper,the effect of finite Larmor radius (FLR) on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic (FLR-MHD) theory.A linear FLR ballooning mode equation is derived in an ’s α’ type equilibrium of circular-flux-surfaces,which is reduced to the ideal ballooning mode equation when the FLR effect is neglected.The present model reproduces some basic features of FLR effects on ballooning mode obtained previously by kinetic ballooning mode theories.That is,the FLR introduces a real frequency into ballooning mode and has a stabilising effect on ballooning modes (e.g.,in the case of high magnetic shear s ≥ 0.8).In particular,some new properties of FLR effects on ballooning mode are discovered in the present research.Here it is found that in a high magnetic shear region (s ≥ 0.8) the critical pressure gradient (α c,FLR) of ballooning mode is larger than the ideal one (α c,IMHD) and becomes larger and larger with the increase of FLR parameter b 0.However,in a low magnetic shear region,the FLR ballooning mode is more unstable than the ideal one,and the α c,FLR is much lower than the α c,IMHD.Moreover,the present results indicate that there exist some new weaker instabilities near the second stability boundary (obtained from ideal MHD theory),which means that the second stable region becomes narrow. 相似文献
3.
This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises.Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the cross-correlated noises are studied.The stationary solutions of the Fokker-Planck equation for three specific examples are analysed.It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions. 相似文献
4.
Zheng-Lin Jia 《International Journal of Theoretical Physics》2009,48(1):226-231
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. 相似文献
5.
Output power spectrum of a single-mode laser driven by coloured pump and quantum noises with coloured correlation
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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
6.
在Levins模型的基础上研究了色交叉关联噪声对集合种群稳定性的影响, 应用Fokker-Plank方程得到了系统的稳态概率密度函数, 运用最快下降法得到了平均灭绝时间的解析式. 结果表明: 两噪声色关联时, 加性噪声强度和乘性噪声强度均弱化集合种群的稳定性; 噪声关联强度强化集合种群的稳定性. 两噪声之间负关联时, 平均灭绝时间是加性噪声强度和乘性噪声强度的减函数, 是噪声关联时间的增函数; 两噪声之间正关联时, 平均灭绝时间是加性噪声强度和噪声关联时间乘性噪声强度的减函数, 是乘性噪声强度的非单调函数.
关键词:
集合种群
色交叉关联噪声
稳定性
平均灭绝时间 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
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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 associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative
coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method,
the analytic expressions of the stationary probability distribution Pst(x), the relaxation time Tc, and the normalized correlation function C(s) of the system are obtained. The effects of the noise intensity, the cross-correlation
strength λ and the cross-correlation time τ are discussed. By numerical computation, it is found that the cross-correlation
strength |λ| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation
time τ delays relaxation of the system from unstable points. The cross-correlation strength λ and the cross-correlation time
τ can alter the effects of the pump noise intensity Q. Thus, the relaxation time Tc is a stochastic resonant phenomenon, and distribution
curves exhibit a single-maximum structure. 相似文献
9.
In this paper, we investigate a mathematical model for describing the growth of tumor cell under immune response, which is
driven by cross-correlation between multiplicative and additive colored noises as well as the nonzero cross-correlation in
between. The expression of the mean first-passage time (MFPT) is obtained by virtue of the steepest-descent approximation.
It is found: (i) When the noises are negatively cross-correlated (λ<0), then the escape is faster than in the case with no correlation (λ=0); when the noises are positively cross-correlated (λ>0), then the escape is slower than in the case with no correlation. Moreover, in the case of positive cross-correlation,
the escape time has a maximum for a certain intensity of one of the noises, i.e., the maximum for MFPT identifies the noise
enhanced stability of the cancer state. (ii) The effect of the cross-correlation time τ
3 on the MFPT is completely opposite for λ>0 and λ<0. (iii) The self-correlation times τ
1 and τ
2 of colored noises can enhance stability of the cancer state, while the immune rate β can reduce it. 相似文献
10.
11.
The stationary correlation function and the associated relaxation time for a general system driven by cross-correlated white noises are derived, by virtue of a Stratonovich-like ansatz. The effects of correlated noises on the relaxation time of a bistable kinetic model coupled to an additive and a multiplicative white noises are studied. It is proved that for small fluctuations the relaxation time T_c as a function of λ (the correlated intensity between noises) exhibits very different behaviours for αD (α and D, respectively, stand for the ntensities of additive and multiplicative noises). When α>D, T_c increases with increasing λ. But when α相似文献
12.
Intensity Correlation Function of a Single-Mode Laser Driven
by Two Colored
Noises with Colored Cross-Correlation 总被引:1,自引:0,他引:1
HANLi-Bo CAOLi WUDa-Jin WANGJun 《理论物理通讯》2004,42(1):59-63
By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. Moreover, we find that there is a minimum Tmin in the curve of the intensity correlation time versus the pump noise intensity, and the depth and position of Train strongly depend on the quantum noise self-correlation time T2 and cross-correlation time T3. 相似文献
13.
研究了受色交叉关联噪声驱动的癌细胞增长系统的平均首通时间.根据Novikov定理和Fox方法得到了相应的近似Fokker-Planck方程,给出了稳态概率密度函数的表达式.运用最快下降法,得到了平均首通时间的解析式.数值结果表明:两噪声之间负关联时,平均首通时间是加性噪声强度和乘性噪声强度的减函数,是噪声关联时间的增函数;两噪声之间正关联时,平均首通时间与加性噪声强度之间的单调关系与穿越方向有关,是乘性噪声强度的非单调函数,是噪声关联时间的减函数. 相似文献
14.
A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time τ and the cross-correlation intensity λ between noises on the normalized intensity correlation function C(s). It is found that if λ> 0 (λ< 0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time τ, and at large value of τ, the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when λ is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when λ becomes smaller and smaller. 相似文献
15.
HAN Li-Bo CAO Li WU Da-Jin WANG Jun 《理论物理通讯》2004,42(7)
By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. T3. 相似文献
16.
Effects of signal modulation and coloured cross-correlation of coloured noises on the diffusion of a harmonic oscillator
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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
17.
《Physics letters. A》2001,291(6):371-375
An analytical investigation of overdamped Brownian particle in a periodic system driven by intensive cross-correlated Gaussian white noises is presented. The center idea of this Letter is to construct an exact soluble model to exhibit the possible new effect of the cross-correlated Gaussian white noises on the noise-induced transport. The model clearly shows the following new aspects of this transport: (1) There is one and only extreme in the J–Q curve for the case of weakly cross-correlated noises here J and Q denote the current and multiplicative noise intensity, respectively. (2) When the two noises are intensive correlative, the J–Q curve behaves three extrema. (3) The J–Q curve exhibits a giant suppression plateau between the two maxima as the noise correlation coefficient is increased further. (4) The direction of the current is controlled by two parameters. 相似文献
18.
Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system
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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. 相似文献
19.
Kang-Kang Wang De-Cai Zong Ya-Jun Wang Sheng-Hong Li 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(5):122
In this paper, the transition between the stable state of a big density and theextinction state and stochastic resonance (SR) for a time-delayed metapopulation systemdisturbed by colored cross-correlated noises are investigated. By applying the fastdescent method, the small time-delay approximation and McNamara and Wiesenfeld’s SRtheory, we investigate the impacts of time-delay, the multiplicative, additive noises andcolored cross-correlated noise on the SNR and the shift between the two states of thesystem. Numerical results show that the multiplicative, additive noises and time-delay canall speed up the transition from the stable state to the extinction state, while thecorrelation noise and its correlation time can slow down the extinction process of thepopulation system. With respect to SNR, the multiplicative noise always weakens the SReffect, while noise correlation time plays a dual role in motivating the SR phenomenon.Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon.Conversely, it could motivate the SR effect to increase the strength of thecross-correlation noise in the SNR-β plot, while the increase of additive noiseintensity will firstly excite SR, and then suppress the SR effect. 相似文献
20.
Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise
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This paper investigates the stochastic resonance (SR) phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon. 相似文献