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1.
The effects of the correlation time τ between noises on the noise-enhanced stability (NES) phenomenon in an asymmetric bistable system driven by cross-correlated noise are investigated. The expressions for the average escape time from the left metastable state TL and from the right metastable state TRare derived. The results indicate that: i) The NES effect is suppressed as the correlation time τ increases for two metastable states; ii) The increase in τ speeds up the escape process from the right state for positively correlated noise, whereas its role is reverses for negatively correlated; iii) In the escape process from the left state, the role of τ is opposite to that in escape from the right state. 相似文献
2.
The velocity variable of a noise oscillator as an internal or
external noise is proposed, the spectrum of which is quite
different from that of the coordinate variable of the same noise
oscillator. The former leads to ballistic diffusion for a free
particle in long time limit and the asymptotical results of the
system are sensitive to the initial condition. However, diffusion
process induced by the coordinate of noise oscillator is a normal
one and depends on the initial condition only in the transient
time. This allows us to classify two kinds of non-Markovian
processes: normal one and strong one, just like the processes
induced by the coordinate and the velocity of noise oscillator,
respectively. Applying to a correlation ratchet, we have found
that the steady current of a particle subjected to the velocity of
noise oscillator is opposite to that subjected to its coordinate,
thus the former shows greenness and the latter redness. 相似文献
3.
The brownian motion in a quartic double-well potential driven by coloured noise is investigated in the low-viscosity limit by means of analogue simulation. The dependence of the escape rate on the noise correlation-time τ is determined for the conditions simulated: the escape rate decreases exponentially with increasing τ2. The relevant law is derived theoretically in the limit of vanishingly small viscosity and high potential barriers. 相似文献
4.
5.
G. Bonanno D. Valenti B. Spagnolo 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(3):405-409
We study a generalization of the Heston model, which consists of
two coupled stochastic differential equations, one for the stock
price and the other one for the volatility. We consider a cubic
nonlinearity in the first equation and a correlation between the
two Wiener processes, which model the two white noise sources.
This model can be useful to describe the market dynamics
characterized by different regimes corresponding to normal and
extreme days. We analyze the effect of the noise on the
statistical properties of the escape time with reference to the
noise enhanced stability (NES) phenomenon, that is the noise
induced enhancement of the lifetime of a metastable state. We
observe NES effect in our model with stochastic volatility. We
investigate the role of the correlation between the two noise
sources on the NES effect. 相似文献
6.
The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed
to obtain the approximate expressions of MFPT. The effects of non-Gaussian
parameter (measures deviation from Gaussian character) r, the delay
time τ, the noise correlation time
τ0, the intensities D and α of noise on the MFPT are discussed. It is found
that the escape time could be reduced by increasing the delay time τ,
the noise correlation time τ0, or by reducing the
intensities D and α. As far as we know, this is the first time to
consider the effect of delay time on the mean first-passage time in the
stochastic dynamical system. 相似文献
7.
Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network
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Spatial coherence resonance in a two-dimensional neuronal network
induced by additive Gaussian coloured noise and parameter diversity
is studied. We focus on the ability of additive Gaussian coloured
noise and parameter diversity to extract a particular spatial
frequency (wave number) of excitatory waves in the excitable medium
of this network. We show that there exists an intermediate noise
level of the coloured noise and a particular value of diversity,
where a characteristic spatial frequency of the system comes forth.
Hereby, it is verified that spatial coherence resonance occurs in
the studied model. Furthermore, we show that the optimal noise
intensity for spatial coherence resonance decays exponentially with
respect to the noise correlation time. Some explanations of the
observed nonlinear phenomena are also presented. 相似文献
8.
This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time τ1 and τ2 by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. (1) The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate μ decides that the selection is propitious to gene A haploid or gene B haploid. (2) The additive coloured noise intensity and the correlation time τ2 play opposite roles. It is noted that α and τ2 can not separate the single peak, while can make the peak disappear and ~-2 can make the peak be sharp. (3) The multiplicative coloured noise intensity D and the correlation time τ1 can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing D and decreasing τ1. 相似文献
9.
Intensity correlation time of a single-mode laser driven by two coloured noises with coloured cross-correlation with direct signal modulation
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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
10.
The effects of colored noise on a new chemical oscillator in CSTR are studied by computer simulation. Colored noise induced nonequilibrium transitions from one limit-cycle to two and more than two limit-cycles when the correlation time and the intensity of noise are varied. Chemical chaos is also observed. 相似文献
11.
Iwaniszewski J Kaufman IK McClintock PV McKane AJ 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(2):1170-1175
Electronic analog experiments on escape over a fluctuating potential barrier are performed for the case when the fluctuations are caused by Ornstein-Uhlenbeck noise (OUN). In its dependence on the relation between the two OUN parameters (the correlation time tau and noise strength Q) the nonmonotonic variation of the mean escape time T as a function of tau can exhibit either a minimum (resonant activation), or a maximum (inhibition of activation), or both these effects. The possible resonant nature of these features is discussed. We claim that T is not a good quantity to describe the resonancelike character of the problem. Independently of the specific relation between the OUN parameters, the resonance manifests itself as a maximal lowering of the potential barrier during the escape event, and it appears for tau of the order of the relaxation time toward the metastable state. 相似文献
12.
Breakup of spiral wave in the Hindmarsh-Rose neurons with nearest-neighbour couplings is reported. Appropriate initial values and parameter regions are selected to develop a stable spiral wave and then the Gaussian coloured noise with different intensities and correlation times is imposed on all neurons to study the breakup of spiral wave, respectively. Based on the mean field theory, the statistical factor of synchronization is defined to analyse the evolution of spiral wave. It is found that the stable rotating spiral wave encounters breakup with increasing intensity of Gaussian coloured noise or decreasing correlation time to certain threshold. 相似文献
13.
Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network. 相似文献
14.
Additive Temporal Coloured Noise Induced Eckhaus Instability in Complex Ginzburg-Landau Equation System
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The effect of additive coloured noises, which are correlated in time, on one-dimensional travelling waves in the complex Ginzburg-Landau equation is studied by numerical simulations. We found that a small coloured noise with temporal correlation could considerably influence the stability of one-dimensional wave trains. There exists an optimal temporal correlation of noise where travelling waves are the most vulnerable. To elucidate the phenomena, we statistically calculated the convective velocities Vg of the wave packets, and found that the coloured noise with an appropriate temporal correlation can decrease Vg, making the system convectively more unstable. 相似文献
15.
Stochastic resonance in a bistable system with coloured correlation between additive and multiplicative noise
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The phenomenon of stochastic resonance (SR) in a bistable nonlinear system with coupling between additive and multiplicative noises is investigated when the correlation between two noise terms is coloured. It is found that the signal-to-noise ratio (SNR) of the system is affected not only by the coupling strength λ between two noise terms, but also by the noise correlation time τ. The SNR is changed from a single peak, to two peaks with a dip, and then to a monotonically decreasing function with noise strength. The dependence of the SR on the initial conditions is entirely caused by the coupling strength λ between two noise terms. 相似文献
16.
C.W. Xie D.C. Mei L. Cao D.J. Wu 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(1):83-86
The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations
between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is
derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER
numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative
noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier
for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated
noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of
the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change.
Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003
RID="a"
ID="a"e-mail: kmdcmei@public.km.yn.cn 相似文献
17.
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
18.
The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts
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Using the linear approximation method, this paper studies the statistical property
of a single-mode laser driven by both coloured pump noise with signal modulation and
the quantum noise with cross-correlation between its real and imaginary parts, and
calculates the steady-state mean normalized intensity fluctuation and intensity
correlation time. It analyses the influences of the modulation signal, the net gain
coefficient, the noise and its correlation form on the statistical fluctuation of
the laser system respectively. It is found that the coloured pump noise modulated by
the signal has a great suppressing action on the statistical fluctuation of the
laser system; the pump noise self-correlation time and the specific frequency of
modulation signal have the result that the statistical fluctuation tends to zero.
Furthermore, the `colour' correlation of pump noise has much influences on the
statistical fluctuation of the laser system. Increasing the intensity of pump noise
will augment the statistical fluctuation of the laser system, but the intensity of
quantum noise and the coefficient of cross-correlation between its real and
imaginary parts have less influence on the statistical fluctuation of the laser
system. Therefore, from the conclusions of this paper the statistical property can
be known and a theoretical basis for steady operation and output of the laser system
can be provided. 相似文献
19.
Kang-Kang Wang Hui Ye Ya-Jun Wang Sheng-Hong Li 《Chinese Journal of Physics (Taipei)》2018,56(5):2191-2203
In this paper, we aim to explore the mean extinction rate and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by a multiplicative periodic signal, colored cross-correlated multiplicative and additive Gaussian noises. By use of the fast descent method and the adiabatic approximation theory for the signal-to-noise ratio, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results indicate that the various SR phenomena occur in the metapopulation system due to the variation of the noise terms and the correlation time. Specifically, the noise correlation always plays a critical role in motivating the SR phenomenon, while the multiplicative noise exerts the inhibition effect on the SR. Interestingly, the weak additive noise can stimulate the resonant peak of the SNR, while the further increase of the noise intensity will lead to the reduction of the SR effect. On the other hand, the noise correlation time τ plays antipodal roles in motivating the SR phenomenon under different circumstances. With regard to the mean extinction rate of the population from the boom state to the extinction one, by performing the numerical calculations, it is found that the additive noise always accelerate the extinction of the population, while the correlation noise will slow down the decline for the population. The role that the noise correlation time plays in the population extinction depends on the values that λ takes. 相似文献