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Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and lévy noise

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Chinese Physics B 2022年第3期31卷 146-159页

作者： liang'an Huo Yafang Dong Business School University of Shanghai for Science and TechnologyShanghai 200093China

The appearance of rumors intensifies people’s panic and affects social stability. How to control the spread of rumors has become an important issue which is worth studying. In order to more accurately reflect the actual situation in the real world, a stochastic model incorporating media coverage and lévy noise is proposed to describe the dynamic process of rumor propagation. By introducing two control strategies of popular science education and media coverage in an emergency event, an near-optimal control problem that minimizes the influence and control cost of rumor propagation is *** conditions for near-optimal control of the model are established by using a Hamiltonian function. Then the necessary conditions for near-optimal control are obtained by using the Pontryagin maximum principle. Finally, the effect of popular science education, media coverage and lévy noise on rumor propagation process control is verified by numerical simulation.

关键词： rumor propagation near-optimal control popular science education media coverage lévy noise

Detecting physical laws from data of stochastic dynamical systems perturbed by non-Gaussianα-stable lévy noise

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Chinese Physics B 2023年第5期32卷 337-342页

作者：陆凌弘志李扬刘先斌 State Key laboratory of Mechanics and Control for Mechanical Structures College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016China School of Automation Nanjing University of Science and TechnologyNanjing 210094China

Massive data from observations,experiments and simulations of dynamical models in scientific and engineering fields make it desirable for data-driven methods to extract basic laws of these *** present a novel method to identify such high dimensional stochastic dynamical systems that are perturbed by a non-Gaussianα-stable lévy *** explicitly,firstly a machine learning framework to solve the sparse regression problem is established to grasp the drift terms through one of nonlocal Kramers–Moyal *** the jump measure and intensity of the noise are disposed by the relationship with statistical characteristics of the *** examples are then given to demonstrate the *** approach proposes an effective way to understand the complex phenomena of systems under non-Gaussian fluctuations and illuminates some insights into the exploration for further typical dynamical indicators such as the maximum likelihood transition path or mean exit time of these stochastic systems.

关键词： data-driven modelling noise-induced transitions lévy noise Kramers–Moyal formuas

Poisson Stable Solutions for Stochastic Differential Equations with lévy noise

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Acta Mathematica Sinica,English Series 2022年第1期38卷 22-54页

作者： Xin lIU Zhen Xin lI School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional l′evy noise with large *** suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of *** we show that these solutions are globally asymptotically stable in square-mean ***,we illustrate our theoretical results by several examples.

关键词： Stochastic differential equation lévy noise periodic solution quasi-periodic solution almost periodic solution levitan almost periodic solution almost automorphic solution Birkhoff recurrent solution Poisson stable solution asymptotic stability

3D shear flows driven by lévy noise at the boundary

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Probability, Uncertainty and Quantitative Risk 2023年第1期8卷 75-94页

作者： Wai-tong(louis)Fan Ali Pakzad Krutika Tawri Roger Temam Department of Mathematics Indiana University BloomingtonIN 47405USA Department of Mathematics California State University NorthridgeCA 91330USA Department of Mathematics University of California BerkeleyCA 94720USA

This paper is concerned with the stochastic incompressible Navier–Stokes equations in a layer of fluid between two flat no-slip *** fluid is driven by the noisy movement of the bottom boundary,where the noise is given by a lévy *** establishing existence of a martingale solution,we use the background flow method to derive an upper bound on the turbulent energy dissipation *** estimate recovers one of the basic scaling ideas of turbulence theory,namely,that the dissipation rate is independent of the viscosity at high Reynolds number.

关键词： Existence lévy noise Navier–Stokes equations 3D shear flows Upper bound

Dynamical Analysis of a Stochastic Predator-Prey System with lévy noise and Impulsive Toxicant Input

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Journal of Applied Mathematics and Physics 2020年第9期8卷 1999-2019页

作者： Xiaowan She Yuanfu Shao Taolin Zhang College of Science Guilin University of Technology Guilin China

This paper established a modified leslie-Gower and Holling-type IV stochastic predator-prey model with lévy noise and impulsive toxicant input. We study the stability in distribution of solutions by inequality techniques and ergodic method. By comparison method and Itô’s formula, we obtain the sufficient conditions for the survival of each species. Some numerical simulations are introduced to show the theoretical results.

关键词： lévy noise Impulsive Toxicant Input Comparison Method Extinction and Persistence

Stochastic modeling and analysis of hepatitis and tuberculosis co-infection dynamics

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Chinese Physics B 2024年第11期33卷 137-153页

作者： Sayed Murad Ali Shah Yufeng Nie Anwarud Din Abdulwasea Alkhazzan Bushra Younas School of Mathematics and Statistics Northwestern Polytechnical UniversityXi'an 710072China Department of Mathematics Sun Yat-sen UniversityGuangzhou 510275China Department of Mathematics University of SialkotP.O.Box 052Pakistan

Several mathematical models have been developed to investigate the dynamics of tuberculosis(TB)and hepatitis B virus(HBV).Numerous current models for TB,HBV,and their co-dynamics fall short in capturing the important and practical aspect of *** is crucial to take into account a stochastic co-infection HBV–TB epidemic model since different random elements have a substantial impact on the overall dynamics of these *** provide a novel stochastic co-model for TB and HBV in this study,and we establish criteria on the uniqueness and existence of a nonnegative global *** also looked at the persistence of the infections as long its dynamics are governable by the proposed *** verify the theoretical conclusions,numerical simulations are presented keeping in view the associated analytical *** infections are found to finally die out and go extinct with certainty when l´evy intensities surpass the specified thresholds and the related stochastic thresholds fall below *** findings also demonstrate the impact of noise on the decline in the co-circulation of HBV and TB in a given *** results provide insights into effective intervention strategies,ultimately aiming to improve the management and control of TB and HBV co-infections.

关键词： tuberculosis(TB) hepatitis B virus(HBV) white noise lévy noise stochastic model

Nonlocal Dynamics for Non-Gaussian Systems Arising in Biophysical Modeling

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Communications on Applied Mathematics and Computation 2020年第2期2卷 201-213页

作者： Xiaoli Chen Jinqiao Duan Center for Mathem atical Sciences and School of Mathematics and Statistics Huazhong University o f Science and TechnologyWuhan 430074China Department of Applied Mathematics Illinois Institute of TechnologyChicagoIL 60616USA

The aim of this article is to review our recent work on nonlocal dynamics of non-Gaussian systems arising in a gene regulatory *** have used the mean exit time,escape probability and maximal likely trajectory to quantify dynamical behaviors of a stochastic diferential system with non-Gaussianα-stable lévy motions,to examine how the nonGaussianity index and noise intensity afect the gene transcription processes.

关键词： Mean exit time Escape probability Nonlocal Fokker-Planck equation Maximal likely trajectory Gene regulation lévy noise