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Daqing Jiang - One of the best experts on this subject based on the ideXlab platform.
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Dynamics of a Stochastic Echinococcosis infection Model
2020Co-Authors: Huina Zhang, Daqing JiangAbstract:This paper is concerned a novel spreading dynamical model for Echinococcosis with stochastic parameter perturbation. we show that there exist a Unique Positive Solution of the stochastic model. Sufficient conditions for the stationary distribution which is ergodic is established by appropriate Lyapunov functions. Furthermore, we obtain the conditions on which the system will extinct. Finally, we illustrate our results by numerical simulation.
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Ergodic property of a Lotka–Volterra predator–prey model with white noise higher order perturbation under regime switching
Applied Mathematics and Computation, 2018Co-Authors: Daqing Jiang, Donal O'regan, Tasawar Hayat, Bashir AhmadAbstract:In this paper, we investigate a classical Lotka–Volterra predator–prey model with telephone noise and a higher order perturbation of white noise. The existence of a Unique Positive Solution is discussed and sufficient conditions for the existence of an ergodic stationary distribution is established. Some simulation figures are presented to illustrate the analytical findings.
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the dynamics of the stochastic multi molecule biochemical reaction model
Journal of Mathematical Chemistry, 2014Co-Authors: Daqing Jiang, Ying Yang, Yanan ZhaoAbstract:The paper introduces the dynamics of a stochastic multi-molecule biochemical reaction model.First, we show that there is a Unique Positive Solution of the stochastic model. Furthermore, we deduce the conditions when the reaction will end and when the reaction being proceed. At last, we derive that the Solution of (1.5) oscillates around the endemic proportion equilibrium \(P^*(x^*,y^*)\), and the intensity of fluctuation is proportional to white noise. The key to the analysis in this paper is choosing appropriate Lyapunov function. The outcomes are illustrated by computer simulations throughout this paper.
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Dynamical Behavior of the Stochastic Delay Mutualism System
Abstract and Applied Analysis, 2014Co-Authors: Peiyan Xia, Daqing JiangAbstract:We discuss the dynamical behavior of the stochastic delay three-specie mutualism system. We develop the technique for stochastic differential equations to deal with the asymptotic property. Using it we obtain the existence of the Unique Positive Solution, the asymptotic properties, and the nonpersistence. Finally, we give the numerical examinations to illustrate our results.
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Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation
Abstract and Applied Analysis, 2014Co-Authors: Daqing Jiang, Donal O'reganAbstract:We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion among patches. First, we show that this system has a Unique Positive Solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.
Ke Wang - One of the best experts on this subject based on the ideXlab platform.
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Analysis on a Stochastic Two-Species Ratio-Dependent Predator-Prey Model
Methodology and Computing in Applied Probability, 2013Co-Authors: Ke Wang, Dongdong ChenAbstract:A stochastic two-species ratio-dependent predator-prey system is investigated. We show that there is a Unique Positive Solution to the model for any Positive initial value. Stochastically ultimate boundedness and uniform continuity are considered. Moreover, under some conditions, we conclude that the stochastic model is persistent in mean and extinct. Finally we introduce some figures to illustrate our main results.
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On a stochastic predator‐prey system with modified functional response
Mathematical Methods in the Applied Sciences, 2011Co-Authors: Ke WangAbstract:A stochastic predator–prey system with modified functional response is investigated. We show that there is a Unique Positive Solution to the model for any Positive initial value by comparison theorem. Moreover, under some conditions, we conclude that the stochastic model is persistent in mean and extinct. Copyright © 2011 John Wiley & Sons, Ltd.
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Asymptotic properties of a stochastic predator–prey system with Holling II functional response☆
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Ke WangAbstract:Abstract A stochastic predator–prey system with Holling II functional response is proposed and investigated. We show that there is a Unique Positive Solution to the model for any Positive initial value. And we show that the Positive Solution to the stochastic system is stochastically bounded. Moreover, under some conditions, we conclude that the stochastic model is stochastically permanent and persistent in mean.
Lishan Liu - One of the best experts on this subject based on the ideXlab platform.
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iterative analysis of the Unique Positive Solution for a class of singular nonlinear boundary value problems involving two types of fractional derivatives with p laplacian operator
Complexity, 2019Co-Authors: Fang Wang, Lishan Liu, Yumei ZouAbstract:This article is concerned with a class of singular nonlinear fractional boundary value problems with p-Laplacian operator, which contains Riemann–Liouville fractional derivative and Caputo fractional derivative. The boundary conditions are made up of two kinds of Riemann–Stieltjes integral boundary conditions and nonlocal infinite-point boundary conditions, and different fractional orders are involved in the boundary conditions and the nonlinear term, respectively. Based on the method of reducing the order of fractional derivative, some properties of the corresponding Green’s function, and the fixed point theorem of mixed monotone operator, an interesting result on the iterative sequence of the Uniqueness of Positive Solutions is obtained under the assumption that the nonlinear term may be singular in regard to both the time variable and space variables. And we obtain the dependence of Solution upon parameter. Furthermore, two numerical examples are presented to illustrate the application of our main results.
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Unique iterative Positive Solutions for a singular p -Laplacian fractional differential equation system with infinite-point boundary conditions
Boundary Value Problems, 2019Co-Authors: Limin Guo, Lishan LiuAbstract:By using the method of mixed monotone operator, a Unique Positive Solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is derived and some useful properties of the Green’s function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the Positive Solutions for the boundary value problem are established. Moreover, the Unique Positive Solution that we obtained in this paper is dependent on $\lambda ,\mu $ , and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.
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Convergence analysis of iterative scheme and error estimation of Positive Solution for a fractional differential equation
Mathematical Modelling and Analysis, 2018Co-Authors: Xinguang Zhang, Lishan Liu, Yujun CuiAbstract:In this paper, we focus on the iterative scheme and error estimation of Positive Solutions for a class of p-Laplacian fractional order differential equation subject to Riemann-Stieltjes integral boundary condition. Under a weaker growth condition of nonlinearity, by using a monotone iterative technique, we first establish a new result on the sufficient condition for the existence of a Unique Positive Solution to the above problem, then construct an iterative scheme which converges to the Unique Positive Solution, and then present an error estimation and the exact convergence rate of the approximate Solution.
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the convergence analysis and error estimation for Unique Solution of a p laplacian fractional differential equation with singular decreasing nonlinearity
Boundary Value Problems, 2018Co-Authors: Xinguang Zhang, Lishan Liu, Yujun CuiAbstract:In this paper, we focus on the convergence analysis and error estimation for the Unique Solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the Unique Positive Solution to the problem is established. Then, from the developed iterative technique, the sequences converging uniformly to the Unique Solution are formulated, and the estimates of the error and the convergence rate are derived.
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Iterative Unique Positive Solutions for singular p-Laplacian fractional differential equation system with several parameters
Nonlinear Analysis: Modelling and Control, 2018Co-Authors: Limin Guo, Lishan LiuAbstract:By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a Unique Positive Solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann–Stieltjes integral boundary conditions. This equation system is very wide because there are many parameters, which can be changeable in the equation system in this paper, and the nonlinearity is allowed to be singular in regard to not only the time variable but also the space variable. Moreover, the Unique Positive Solution that we obtained in this paper is dependent on λ, and an iterative sequence and convergence rate are given, which are important for practical application. An example is given to demonstrate the application of our main results.
Zhongxin Zhang - One of the best experts on this subject based on the ideXlab platform.
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singular nonlinear boundary value problems arising in boundary layer theory
Journal of Mathematical Analysis and Applications, 1999Co-Authors: Junyu Wang, Zhongxin ZhangAbstract:Abstract The singular nonlinear boundary value problem [equation] arises in the boundary layer theory. We prove in this paper that the problem has a Unique Positive Solution for each fixed λ ≥ 0 and there is no Positive Solution for λ ≤ −1/2.
Yingjia Guo - One of the best experts on this subject based on the ideXlab platform.
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The Stability of Solutions for a Fractional Predator-Prey System
Abstract and Applied Analysis, 2014Co-Authors: Yingjia GuoAbstract:We study a class of fractional predator-prey systems with Holling II functional response. A Unique Positive Solution of this system is obtained. In order to prove the asymptotical stability of Positive equilibrium for this system, we study the Lyapunov stability theory of a fractional system.
