Asymptotic Properties of a Lotka-Volterra Competition and Mutualism Model Under Stochastic Perturbations

2021 ◽  
Author(s):  
Leonid Shaikhet ◽  
Andrei Korobeinikov
Keyword(s):  
Asymptotic Properties ◽  
Stochastic Perturbations ◽  
Mutualism Model

scholarly journals Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3013
Author(s):  
Leonid Shaikhet
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Wide Class ◽  
Asymptotic Properties ◽  
Nonlinear Mathematical Model ◽  
Simple Criterion ◽  
Stochastic Perturbations ◽  
Food Engineering ◽  
Nonlinear Mathematical Models

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document