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1.
In this article, we discuss the mean first-passage time for non-Markovian processes driven by continuous noise. Applying the iterative method to the Volterra integral equation, we obtain for the first time the series solution to the mean first-passage time problem and present the exact expression for the mean first-passage time in both the cases of rectangular distribution and long-tail distribution. 相似文献
2.
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
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4.
In this Letter, we derive a relationship between the moments of the first-passage time for a random walk and the first-passage time density for subdiffusive processes modeled by continuous-time random walks. In particular, we show that the exact long-time behavior of the density depends only on the mean first-passage time of the corresponding normal diffusive process. In addition, we give explicit evaluations of the first-passage time distribution for general three-dimensional bounded domains. These results are relevant to systems involving anomalous diffusion in confinements. 相似文献
5.
Huiqing Zhang 《Physica A》2009,388(6):781-788
In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker-Planck equation, and the expressions of stationary probability density function and mean first-passage time are presented. Also we explore the effects of correlation between non-Gaussian and Gaussian noise for the mean first-passage time. 相似文献
6.
Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises: Mean First-Passage Time 总被引:1,自引:0,他引:1
LI Dong-Xi XU Wei GUO Yong-Feng LI Gao-Jie 《理论物理通讯》2008,50(9):669-673
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 to, the intensities D and a 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.
研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中, 噪声强度和相关时间对平均首次穿越时间的影响. 利用一致有色噪声近似方法和最速下降方法, 推导出系统平均首次穿越时间的表达式. 研究结果表明: 系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构, 即“共振”现象, 峰值会随着加性噪声强度和噪声之间关联强度的增加而减小. 而平均首次穿越时间作为加性噪声的函数呈单调曲线, 说明乘性噪声和加性噪声对平均首次穿越时间的影响不同. 此外, 乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时 对系统平均首次穿越时间的影响是不同的.
关键词:
色噪声
分段非线性系统
平均首次穿越时间 相似文献
8.
Stochastic properties coupling between of tumor growth with non-Gaussian and Gaussian noise terms
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Dynamical behavior of a tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect. 相似文献
9.
O. Bénichou D. S. Grebenkov P. E. Levitz C. Loverdo R. Voituriez 《Journal of statistical physics》2011,142(4):657-685
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain,
for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented
approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which
provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model
of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption
rate from the surface. 相似文献
10.
Stochastic properties of tumor growth with coupling between non-Gaussian and Gaussian noise terms
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Dynamical behavior of tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect. 相似文献
11.
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
12.
First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system. 相似文献
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We continue the study of a nonlinear first-order dynamical system first considered by Chen. This model is characterized by a multiplicative periodic forcing term and additive dichotomous noise in place of the white noise of Chen's analysis. Two parameters are used to characterize the qualitative properties of such a system, the mean first-passage time to the ends of the interval and the Fourier spectrum generated by the solution of the equation. We show that the mean first-passage time is monotonic in the amplitude of the periodic force and exhibits a resonant dependence on its frequency. In addition the substitution of dichotomous for white noise leads to a systematic change in the ability to smooth out the peaks in the Fourier spectrum of the solution. 相似文献
15.
A method for calculating the mean first-passage time for non-Markovian free processes driven by continuous noise is generalized to free process X(t)=g[F(t)] and unfree process X( t)=f[X(t)]g[F(t)] with nonlinear noise. When the switch distribution + rectangular, the exact analytic expressions of the mean first-passage time for free process X(t) = [F(t)]m driven by nonlinear noise and X( t=) -k[X(t)]n[F(t)lm+ [F(t)]m driven by both multiplicative and nonlinear additive noises are also given. 相似文献
16.
J.-F. Rupprecht O. Bénichou D. S. Grebenkov R. Voituriez 《Journal of statistical physics》2012,147(5):891-918
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We generalize the results of Bénichou et al. in (J. Stat. Phys. 142:657, 2011) and consider a biased diffusion in a general annulus with an arbitrary number of regularly spaced targets on a partially reflecting surface. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface. 相似文献
17.
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
18.
The first-passage problem associated with snap-through of a shallow cylindrical shell subjected to a wide-band stationary stochastic loading is examined in this paper. The structure is sufficiently flat so as to exhibit only a symmetric mode under the action of the applied load. The approach utilizes a high-speed simulation technique to obtain sufficient samples from which statistics of the response may be computed. This allows the calculation of an approximate probability distribution for the parameter of interest. Zero initial conditions are assumed so that the problem is non-stationary. Results of this analysis are compared with the mean first-passage time obtained by numerically solving the associated Pontriagin-Vitt equation. 相似文献
19.
《Physics letters. A》1988,133(9):476-482
We investigate a stochastic differential equation (SDE) with general nonlinearity in the noise. We derive an integro-differential equation for the probability density (PD) and an approximate equation for the mean first-passage time (MFPT). The approximate Fokker-Planck equation (AFPE) and MFPT are obtained for some examples. 相似文献
20.
In this Letter, we develop an analytical approach which provides an explicit determination of mean first-passage times (MFPTs) for random walks in bounded domains for a wide class of transport processes. In particular, we derive for the first time explicit expressions of MFPTs for emblematic models of transport in complex media, such as diffusion on deterministic and random fractals. This approach relies on a scale-invariance hypothesis and a large volume expansion of the MFPT, which actually proves to be very accurate even for small system sizes as shown by numerical simulations. This explicit determination of MFPTs can be straightforwardly generalized to further useful first-passage observables such as occupation times and splitting probabilities. 相似文献