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Lévy noise induced stochastic resonance in an FHN model

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Science China(Technological Sciences) 2016年第3期59卷 371-375页

作者： WANG ZhanQing XU Yong YANG Hui Department of Applied Mathematics Northwestern Polytechnical University Department of Life Sciences Northwestern Polytechnical University

This paper aims to investigate the stochastic resonance （SR） in an FitzHugh-Nagumo （FHN） model with an additive levy noise numerically. The non-Gaussian levy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio （SNR）, and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the levy noise and the FHN model on the SR will be exam- ined, and some mechanisms of the levy noise-induced SR are presented which are different from those of the Gaussian noise.

关键词： levy noise stochastic resonance signal-to-noise ratio FHN model

The Global Attraction of Logistic Equation with Lévy noise

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Journal of Mathematical Research with Applications 2021年第3期41卷 323-330页

作者： Yan WANG School of Mathematical Sciences Dalian University of Technology

The logistic equation with Lévy noise is considered. Under suitable conditions, the global existence and uniqueness is obtained; it is shown that the unique positive equilibrium is globally attractive if the initial ... 详细信息

关键词： Logistic equation levy noise global attraction equilibrium

Effects of Lvy noise and immune delay on the extinction behavior in a tumor growth model

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Chinese Physics B 2014年第9期23卷 126-132页

作者：郝孟丽徐伟谷旭东戚鲁媛 Department of Applied Mathematics Northwestern Polytechnical University

The combined effects of Ltvy noise and immune delay on the extinction behavior in a tumor growth model are explored, The extinction probability of tumor with certain density is measured by exit probability. The expression of the exit probability is obtained using the Taylor expansion and the infinitesimal generator theory. Based on numerical calculations, it is found that the immune delay facilitates tumor extinction when the stability index α〈 1, but inhibits tumor extinction when the stability index α 〉 1. Moreover, larger stability index and smaller noise intensity are in favor of the extinction for tumor with low density. While for tumor with high density, the stability index and the noise intensity should be reduced to promote tumor extinction.

关键词： exit probability levy noise immune delay tumor growth model

Analysis on stochastic dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response

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International Journal of Biomathematics 2021年第2期14卷 1-14页

作者： Shufen Zhao School of Mathematics and Statistics Taishan University525 Dongyue StreetTaishan 271000P.R.China

In this paper,stochastic dynamics with Lévy noise of two-consumers-one-resource competing systems with Beddington–DeAngelis functional response are *** first show the existence of the global positive solution,then discuss the effects of noises on the extinction of the species and the stochastic persistence of the *** the meanwhile,numerical simulations are carried to support ***,we show the existence of the stationary distribution for a special case.

关键词： levy noise stochastic persistence stationary distribution

Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and levy Jumps

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Journal of Donghua University(English Edition) 2014年第3期31卷 217-223页

作者：臧彦超李俊平 School of Mathematics and Statistics Henan University of Science and Technology School of Mathematics and Statistics Central South University

A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0 1,it fluctuates around the endemic equilibrium of the deterministic model.

关键词： susceptible-infective-recovered-susceptible(SIRS) epidemic model levy noise stochastic ultimate boundedness asymptotic behavior

Well-posedness for the stochastic 2D primitive equations with Lévy noise

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Science China Mathematics 2013年第8期56卷 1629-1645页

作者： SUN ChengFeng GAO HongJun Department of Applied Mathematics Nanjing University of Finance and Economics Jiangsu Provincial Key Laboratory for NSLSCS School of Mathematical SciencesNanjing Normal University

The two-dimensional primitive equations with Lévy noise are studied in this *** prove the existence and uniqueness of the solutions in a fixed probability space which based on a priori estimates,weak convergence meth... 详细信息

关键词： primitive equation levy noise existence and uniqueness

Dynamic characterization of a stochastic SIR infectious disease model with dual perturbation

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International Journal of Biomathematics 2021年第4期14卷 1-26页

作者： Driss Kiouach Yassine Sabbar LPAIS Laboratory Faculty of Sciences Dhar El Mahraz Sidi Mohamed Ben Abdellah UniversityFezMorocco

Environmental perturbations are unavoidable in the propagation of infectious *** this paper,we introduce the stochasticity into the susceptible-infected recovered(SIR)model via thc^parameter perturbation *** stochastic disturbances associated with the disease transmission coefficient and the mortality rate are presented with two perturbations:Gaussian white noise and levy jumps,*** idea provides an overview of disease dynamics under different random perturbation *** using new techniques and methods,we study certain interesting asymptotic properties of our perturbed model,namely:persistence in the mean,ergodicity and extinction of the *** illustrative purposes,numerical examples are presented for checking the theoretical study.

关键词： SIR epidemic model white noise levy noise stationary distribution persistence extinction

Dynamic of a stochastic delayed one-predator two-prey model with Lévy jumps in polluted environments

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International Journal of Biomathematics 2021年第1期14卷 125-150页

作者： Yongxin Gao Nana Wang Shiquan Tian College of Science Civil Aviation University of ChinaTianjin 300300P.R.China

This paper is concerned with a stochastic delayed one-predator two-prey model with Lévy jumps in polluted ***,under some simple assumptions,we prove that there exists a unique global nonnegative solution which is permanent in time ***,sufficient criteria for the extinction of each species are ***,we carry out some numerical simulations to verify the theoretical results.

关键词： One-predator two-prey model delay white noise levy noise toxicant

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随机微分方程解的遍历性

随机微分方程解的遍历性

作者：董一林中国科学技术大学

学位级别：硕士

本文给出了距离空间上一般马氏半群的强Feller性蕴含其遍历测度拓扑支撑不交的一个简单证明。由此,可以减弱不变测度唯一所需的相应马氏过程不可约性的要求。之后,证明了由levy噪声驱动的带局部Lipschitz条件的非退化随机微分方程的遍历... 详细信息

本文给出了距离空间上一般马氏半群的强Feller性蕴含其遍历测度拓扑支撑不交的一个简单证明。由此,可以减弱不变测度唯一所需的相应马氏过程不可约性的要求。之后,证明了由levy噪声驱动的带局部Lipschitz条件的非退化随机微分方程的遍历性,并给出了一些例子。最后,对退化的随机微分方程解是否具有强Feller性进行了分析,用Malliavian矩阵的可逆与不可逆情形,分别得到了相应马氏半群的梯度估计,证明了在Malliavain矩阵可逆的情况下,马氏半群具有强Feller性。

关键词：遍历性 levy noise 局部Lipschitz系数李雅普诺夫函数不变测度