scholarly journals The first passage problem for stable linear delay equations perturbed by power law Lévy noise

2019 ◽  
Vol 29 (6) ◽  
pp. 063104
Author(s):  
Michael A. Högele ◽  
Ilya Pavlyukevich
Keyword(s):  
Power Law ◽  
Delay Equations ◽  
Lévy Noise ◽  
First Passage ◽  
Linear Delay ◽  
Levy Noise ◽  
First Passage Problem ◽  
Stable Linear

Dynamical behavior of simplified FitzHugh–Nagumo neural system with time delay driven by Lévy noise

2021 ◽  
pp. 2150240
Author(s):  
Weida Qiu ◽  
Yongfeng Guo ◽  
Xiuxian Yu
Keyword(s):  
Time Delay ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Passage Time ◽  
Neural System ◽  
The Other ◽  
Lévy Noise ◽  
First Passage ◽  
Levy Noise ◽  
System With Time Delay

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

STOCHASTIC PROPERTIES OF TUMOR GROWTH DRIVEN BY WHITE LÉVY NOISE

2012 ◽  
Vol 26 (23) ◽  
pp. 1250149 ◽  
Author(s):  
LILI JIANG ◽  
XIAOQIN LUO ◽  
DAN WU ◽  
SHIQUN ZHU
Keyword(s):  
Tumor Growth ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Gaussian White Noise ◽  
Passage Time ◽  
Lévy Noise ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Levy Noise

The dynamical behavior of tumor growth model driven by Lévy noise terms is investigated. For α = 2 and β = 0, the process driven by white Lévy noise approach to the standard Gaussian white noise can be viewed in the analysis of the steady-state probability distribution and the mean first-passage time. When β → 0, the index α would increase the mean first-passage time as scale σ < 0 and shorten the mean first-passage time as scale σ > 0. A nonzero β parameter induces α to decrease the mean first-passage time. Thus analyzing the initial situation of tumor is very important to obtain more therapy time.

scholarly journals On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations

2016 ◽  
Vol 54 (3) ◽  
pp. 1840-1872 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Chaman Kumar ◽  
Sotirios Sabanis
Keyword(s):  
Delay Equations ◽  
Lévy Noise ◽  
Levy Noise

First-passage behavior of under-damped asymmetric bistable system driven by Lévy noise

2020 ◽  
Vol 34 (31) ◽  
pp. 2050348
Author(s):  
Xiuxian Yu ◽  
Yongfeng Guo ◽  
Xiaojuan Lou ◽  
Qiang Dong
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
Bistable System ◽  
Lévy Noise ◽  
Mean First Passage Time ◽  
First Passage ◽  
System Parameters ◽  
Text Response ◽  
The Mean ◽  
Levy Noise

In this paper, the first-passage behavior of under-damped asymmetric bistable system driven by Lévy noise is studied. The two aspects considered are the mean first-passage time (MFPT) and the distribution of first-passage time in two opposite directions. To begin with, using the Janicki–Weron algorithm to generate Lévy noise, the system driven by Lévy noise is simulated through the fourth-order Runge–Kutta algorithm. Then the first-passage time of [Formula: see text] response tracks is calculated, and the MFPT and the distribution of first-passage time are obtained. Finally, the influence of Lévy noise and system parameters on MFPT and the distribution of first-passage time are analyzed. Moreover, the noise enhanced stability (NES) effect is found.

scholarly journals Stability of linear delay equations under a small noise

1986 ◽  
Vol 29 (2) ◽  
pp. 233-254 ◽  
Author(s):  
S. E. A. Mohammed
Keyword(s):  
White Noise ◽  
Linear Systems ◽  
Stochastic Stability ◽  
Heat Bath ◽  
Delay Equations ◽  
Asymptotically Stable ◽  
Brownian Movement ◽  
Small Noise ◽  
Linear Delay ◽  
Stable Linear

The stochastic stability of linear systems driven by white noise has been treated by several authors e.g. Has'minskii [7], Kushner [11], Kleimann and Arnold [9], Pinsky, [14], Friedman and Pinsky [4], Itô and Nisio [8] , Mohammed [13]. Following R. Kubo [10, 1966], the Brownian movement of a molecule in a “heat bath” is modelled in [4, pp. 223–226] by an asymptotically stable linear f.d.e. which is forced by white noise.

scholarly journals An Enhanced Intrinsic Time-Scale Decomposition Method Based on Adaptive Lévy Noise and Its Application in Bearing Fault Diagnosis

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 617
Author(s):  
Jianpeng Ma ◽  
Shi Zhuo ◽  
Chengwei Li ◽  
Liwei Zhan ◽  
Guangzhu Zhang
Keyword(s):  
Fault Diagnosis ◽  
Time Scale ◽  
Lévy Noise ◽  
Model Parameters ◽  
Rolling Bearings ◽  
Intrinsic Time ◽  
Time Scale Decomposition ◽  
Weak Fault ◽  
Levy Noise ◽  
The Impact

When early failures in rolling bearings occur, we need to be able to extract weak fault characteristic frequencies under the influence of strong noise and then perform fault diagnosis. Therefore, a new method is proposed: complete ensemble intrinsic time-scale decomposition with adaptive Lévy noise (CEITDALN). This method solves the problem of the traditional complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN) method not being able to filter nonwhite noise in measured vibration signal noise. Therefore, in the method proposed in this paper, a noise model in the form of parameter-adjusted noise is used to replace traditional white noise. We used an optimization algorithm to adaptively adjust the model parameters, reducing the impact of nonwhite noise on the feature frequency extraction. The experimental results for the simulation and vibration signals of rolling bearings showed that the CEITDALN method could extract weak fault features more effectively than traditional methods.

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