scholarly journals First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises

2021 ◽  
Author(s):  
Nicholas Mwilu Mutothya ◽  
Yong Xu ◽  
Yongge Li ◽  
Ralf Metzler ◽  
Nicholas Muthama Mutua
Keyword(s):  
Diffusion Coefficient ◽  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Stochastic Motion ◽  
First Passage ◽  
The Mean ◽  
Non Gaussian ◽  
Markovian Systems

Abstract We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' $q$-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times are recorded. The first passage time density is determined along with the mean first passage time. Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the mean first passage time are discussed.

TRANSIENT PROPERTIES OF A BISTABLE KINETIC SYSTEM WITH TIME-DELAYED FEEDBACK AND NON-GAUSSIAN NOISE: MEAN FIRST-PASSAGE TIME

2008 ◽  
Vol 22 (27) ◽  
pp. 2677-2687 ◽  
Author(s):  
CAN-JUN WANG ◽  
DONG-CHENG MEI
Keyword(s):  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Non Gaussian ◽  
Time Delayed Feedback

The transient properties of a bistable system with time-delayed feedback and non-Gaussian noise are investigated. The explicit expressions of the mean first-passage time (MFPT) are obtained. The numerical computations show that the MFPT of the system is affected by the delay time τ, the non-extensive index q and the color noise correlation time τ0. That is, q can induce the MFPT from a complex behavior to a simple monotonous behavior with τ increasing (i.e. from two extrema to no extremum). But with the q increasing, the MFPT has a extremum, which is more large as τ increases.

The mean first-passage time in simplified FitzHugh–Nagumo neural model driven by correlated non-Gaussian noise and Gaussian noise

2018 ◽  
Vol 32 (28) ◽  
pp. 1850339 ◽  
Author(s):  
Yong-Feng Guo ◽  
Bei Xi ◽  
Fang Wei ◽  
Jian-Guo Tan
Keyword(s):  
Gaussian Noise ◽  
Noise Intensity ◽  
First Passage Time ◽  
Neural Model ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Model Driven ◽  
The Mean ◽  
Non Gaussian

In this paper, the mean first-passage time (MFPT) in simplified FitzHugh–Nagumo (FHN) neural model driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise is studied. Firstly, using the path integral approach and the unified colored-noise approximation (UCNA), the analytical expression of the stationary probability distribution (SPD) is derived, and the validity of the approximation method employed in the derivation is checked by performing numerical simulation. Secondly, the expression of the MFPT of the system is obtained by applying the definition and the steepest-descent method. Finally, the effects of the multiplicative noise intensity D, the additive noise intensity Q, the noise correlation time [Formula: see text], the cross-correlation strength [Formula: see text] and the non-Gaussian noise deviation parameter q on the MFPT are discussed.

ESCAPE THROUGH A FLUCTUATING ENERGY BARRIER IN THE PRESENCE OF NON-GAUSSIAN NOISE

2007 ◽  
Vol 07 (02) ◽  
pp. L151-L161 ◽  
Author(s):  
GURUPADA GOSWAMI ◽  
PRADIP MAJEE ◽  
BIDHAN CHANDRA BAG
Keyword(s):  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Resonant Condition ◽  
Non Gaussian ◽  
Turnover Behavior ◽  
Resonant Activation ◽  
Limiting Value

In this paper we have studied how barrier crossing dynamics is affected by colored additive non-Gaussian noise if the barrier fluctuates deterministically. Our investigation indicates that resonant activation(RA) is either enhanced or it becomes robust if noise characteristic is deviated from the Gaussian behavior. We find that additive colored non Gaussian noise can induce the RA-like phenomenon. Another interesting observation is that the turnover behavior persists even in presence of barrier fluctuations at finite rate. Finally, it is observed that mean first passage time(MFPT) decreases with increase of non-Gaussian characteristic of the additive colored noise for a given noise strength and noise correlation time and ultimately reaches to a limiting value. The limiting value remains almost the same if the barrier fluctuating frequency is zero or far from the resonant condition. But near the resonant condition the mean first passage time initially decreases and then increases passing through a minimum as the non Gaussian parameter grows.

scholarly journals Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

2017 ◽  
Vol 16 (01) ◽  
pp. 1750007 ◽  
Author(s):  
Yan-Mei Kang ◽  
Xi Chen ◽  
Xu-Dong Lin ◽  
Ning Tan
Keyword(s):  
Stochastic Resonance ◽  
Gaussian Noise ◽  
Noise Intensity ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage ◽  
Transcriptional Regulatory ◽  
Heavy Tailed ◽  
Non Gaussian

The mean first passage time (MFPT) in a phenomenological gene transcriptional regulatory model with non-Gaussian noise is analytically investigated based on the singular perturbation technique. The effect of the non-Gaussian noise on the phenomenon of stochastic resonance (SR) is then disclosed based on a new combination of adiabatic elimination and linear response approximation. Compared with the results in the Gaussian noise case, it is found that bounded non-Gaussian noise inhibits the transition between different concentrations of protein, while heavy-tailed non-Gaussian noise accelerates the transition. It is also found that the optimal noise intensity for SR in the heavy-tailed noise case is smaller, while the optimal noise intensity in the bounded noise case is larger. These observations can be explained by the heavy-tailed noise easing random transitions.

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