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326 results on '"Jiang, Daqing"'

1. Stochastic generalized Kolmogorov systems with small diffusion: II. Explicit approximations for periodic solutions in distribution

Author

Zhou, Baoquan, Wang, Hao, Wang, Tianxu, and Jiang, Daqing

Subjects
Mathematics - Dynamical Systems, 37H05, 37H30, 45M15, 60H10
Abstract

This paper is Part II of a two-part series on coexistence states study in stochastic generalized Kolmogorov systems under small diffusion. Part I provided a complete characterization for approximating invariant probability measures and density functions, while here, we focus on explicit approximations for periodic solutions in distribution. Two easily implementable methods are introduced: periodic normal approximation (PNOA) and periodic log-normal approximation (PLNA). These methods offer unified algorithms to calculate the mean and covariance matrix, and verify positive definiteness, without additional constraints like non-degenerate diffusion. Furthermore, we explore essential properties of the covariance matrix, particularly its connection under periodic and non-periodic drift coefficients. Our new approximation methods significantly relax the minimal criteria for positive definiteness of the solution of the discrete-type Lyapunov equation. Some numerical experiments are provided to support our theoretical results., Comment: 39 pages, 5 figures

Published
2024

12. Dynamics and numerical simulations of a generalized mosquito-borne epidemic model using the Ornstein-Uhlenbeck process: Stability, stationary distribution, and probability density function.

Author

Niu, Wenhui, Zhang, Xinhong, and Jiang, Daqing

Subjects
MOSQUITO-borne diseases, EPIDEMIOLOGICAL models, COMMUNICABLE diseases, PROBABILITY density function, PERTURBATION theory
Abstract

In this paper, we proposed a generalized mosquito-borne epidemic model with a general nonlinear incidence rate, which was studied from both deterministic and stochastic insights. In the deterministic model, we proved that the endemic equilibrium was globally asymptotically stable when the basic reproduction number R 0 was greater than unity and the disease free equilibrium was globally asymptotically stable when R 0 was lower than unity. In addition, considering the effect of environmental noise on the spread of infectious diseases, we developed a stochastic model in which the infection rates were assumed to satisfy the mean-reverting log-normal Ornstein-Uhlenbeck process. For this stochastic model, two critical values, known as R 0 s and R 0 E , were introduced to determine whether the disease will persist or die out. Additionally, the exact probability density function of the stationary distribution near the quasi-equilibrium point was obtained. Numerical simulations were conducted to validate the results obtained and to examine the impact of stochastic perturbations on the model. In this paper, we proposed a generalized mosquito-borne epidemic model with a general nonlinear incidence rate, which was studied from both deterministic and stochastic insights. In the deterministic model, we proved that the endemic equilibrium was globally asymptotically stable when the basic reproduction number was greater than unity and the disease free equilibrium was globally asymptotically stable when was lower than unity. In addition, considering the effect of environmental noise on the spread of infectious diseases, we developed a stochastic model in which the infection rates were assumed to satisfy the mean-reverting log-normal Ornstein-Uhlenbeck process. For this stochastic model, two critical values, known as and , were introduced to determine whether the disease will persist or die out. Additionally, the exact probability density function of the stationary distribution near the quasi-equilibrium point was obtained. Numerical simulations were conducted to validate the results obtained and to examine the impact of stochastic perturbations on the model. [ABSTRACT FROM AUTHOR]

Published
2024
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27. Asymptotic behavior of a stochastic SIR model with general incidence rate and nonlinear Lévy jumps

Author

Yang, Qing, Zhang, Xinhong, and Jiang, Daqing

Subjects
Original Paper, Control and Systems Engineering, Applied Mathematics, Mechanical Engineering, Lévy jumps, Aerospace Engineering, Ocean Engineering, Extinction, SIR model, Ergodic stationary distribution, Electrical and Electronic Engineering, Incidence rate
Abstract

In this paper, we consider a stochastic SIR epidemic model with general disease incidence rate and perturbation caused by nonlinear white noise and L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\acute{e}$$\end{document}e´vy jumps. First of all, we study the existence and uniqueness of the global positive solution of the model. Then, we establish a threshold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}λ by investigating the one-dimensional model to determine the extinction and persistence of the disease. To verify the model has an ergodic stationary distribution, we adopt a new method which can obtain the sufficient and almost necessary conditions for the extinction and persistence of the disease. Finally, some numerical simulations are carried out to illustrate our theoretical results.

Published
2022

34. Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching.

Author

Wang, Quan, Zu, Li, Jiang, Daqing, and O'Regan, Donal

Subjects
STOCHASTIC systems, PREDATION, LYAPUNOV functions, STOCHASTIC models, WHITE noise, COMPUTER simulation, TELEGRAPH & telegraphy
Abstract

In this paper, by introducing environmental white noise and telegraph noise, we proposed a stochastic predator–prey model with the Beddington–DeAngelis type functional response and investigated its dynamical behavior. Persistence and extinction are two core contents of population model research, so we analyzed these two properties. The sufficient conditions of the strong persistence in the mean and extinction were established and the threshold between them was obtained. Moreover, we took stability into account and, by means of structuring a suitable Lyapunov function with regime switching, we proved that the stochastic system has a unique stationary distribution. Finally, numerical simulations were used to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Published
2023
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