Analysis of a mutualism model with time-related coefficients in a stochastic environment

2020 ◽  
pp. 2050073
Author(s):  
Jun Wei Luo ◽  
Mei Li ◽  
Kai Liu ◽  
Rui Guan
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Existence And Uniqueness ◽  
Uniform Continuity ◽  
Stochastic Environment ◽  
Stochastic Perturbations ◽  
Stochastic Permanence ◽  
Stochastic Boundedness ◽  
Mutualism Model

In this paper, a mutualism model with stochastic perturbations is considered and some of its coefficients are related to time. Under some assumptions, we make efforts to prove the existence and uniqueness of a positive solution, and the asymptotic behavior to the problem is discussed. Furthermore, we also prove the properties of stochastic boundedness, uniform continuity and stochastic permanence of this system. At last, some numerical simulations are introduced to illustrate our main results.

scholarly journals Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Huili Xiang ◽  
Zhuang Fang ◽  
Zuxiong Li ◽  
Zhijun Liu
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Stochastic Differential Equations ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Environmental Noise ◽  
Competitive System ◽  
Stochastic Boundedness

A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

scholarly journals Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qiaoqin Gao ◽  
Zhijiang Luo ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Matrix Method ◽  
Lyapunov Method ◽  
Markovian Switching ◽  
Dynamics Analysis ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Global Positive Solution ◽  
Theoretical Results

This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.

The asymptotic behavior of a stochastic multigroup SIS model

2018 ◽  
Vol 11 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Endemic Equilibrium ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Theoretical Results

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

scholarly journals Analysis of a mutualism model with stochastic perturbations

2015 ◽  
Vol 08 (06) ◽  
pp. 1550072 ◽  
Author(s):  
Mei Li ◽  
Hongjun Gao ◽  
Chenfeng Sun ◽  
Yuezheng Gong
Keyword(s):  
Ecological Model ◽  
Local Existence ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Stochastic Perturbations ◽  
Stochastic Permanence ◽  
Local Existence And Uniqueness ◽  
Mutualism Model ◽  
Stochastically Bounded ◽  
Uniformly Continuous

This paper is concerned with a mutualism ecological model with stochastic perturbations. The local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is studied. Moreover, we show that the solution is stochastically bounded, uniformly continuous and stochastic permanence. The sufficient conditions for the system to be extinct are given and the conditions for the system to be persistent are also established. At last, some figures are presented to illustrate our main results.

scholarly journals Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Panpan Wang ◽  
Jianwen Jia
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Stationary Distribution ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Incidence Rates ◽  
Saturated Incidence ◽  
Global Positive Solution

Abstract In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.

Asymptotic Behavior of a Stochastic Two-Species Competition System with Impulsive Effects

2018 ◽  
Vol 19 (5) ◽  
pp. 427-438
Author(s):  
Pan Wang ◽  
Bing Li ◽  
Yongkun Li
Keyword(s):  
Asymptotic Behavior ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Species Competition ◽  
Stochastic Permanence ◽  
Competition System ◽  
Stochastic Boundedness ◽  
Dynamical Properties ◽  
Persistent In Mean

AbstractIn this paper, we consider a stochastic two-species competition system with impulsive effects. Some dynamical properties are investigated and sufficient conditions for the stochastic boundedness, stochastic permanence and global attractivity are established. Under some conditions, we conclude that the stochastic model is persistent in mean and extinction. An example is given to illustrate the main result.

scholarly journals Asymptotic behavior of a stochastic HIV model with Beddington–DeAngelis functional response

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Suxia Wang ◽  
Juan Zhao ◽  
Junxing Zhu ◽  
Xiaoli Ren
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Functional Response ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Hiv Model ◽  
Stochastically Stable ◽  
Global Positive Solution

Abstract In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the infected steady state of the corresponding deterministic HIV model. Finally, some numerical simulations are carried out to verify our results.

scholarly journals A Uniqueness Result for a Simple Superlinear Eigenvalue Problem

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Michael Herrmann ◽  
Karsten Matthies
Keyword(s):  
Eigenvalue Problem ◽  
Numerical Simulations ◽  
Convolution Operator ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Constitutive Laws ◽  
Parameter Family ◽  
Shape Constraint ◽  
Special Case ◽  
Nonlinear Eigenfunctions

AbstractWe study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological shape constraint. Our proof uses a nonlinear change of scalar parameters and applies Krein–Rutman arguments to a linear substitute problem. We also present numerical simulations and discuss the asymptotics of two limiting cases.

scholarly journals A Stochastic SIR Epidemic System with a Nonlinear Relapse

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ali El Myr ◽  
Abdelaziz Assadouq ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aadil Lahrouz
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Spread Model ◽  
Stochastic Sir ◽  
Theoretical Results

We investigate the conditions that control the extinction and the existence of a unique stationary distribution of a nonlinear mathematical spread model with stochastic perturbations in a population of varying size with relapse. Numerical simulations are carried out to illustrate the theoretical results.

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