Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects

Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects

In this paper, the Lotka-Volterra 3-species mutualism models with diffusion and delay effects is investigated. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the unique positive steady-state solution of the corresponding steady-state problem in a bound...

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Main Authors: Chang-you Wang, Shu Wang, Xiang-ping Yan
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2009/317298
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spelling doaj-8e7cb3bd1f294c36bbef76e914f9f2ac2020-11-24T23:00:30ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/317298317298Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay EffectsChang-you Wang0Shu Wang1Xiang-ping Yan2College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaCollege of Applied Sciences, Beijing University of Technology, Beijing 100124, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, ChinaIn this paper, the Lotka-Volterra 3-species mutualism models with diffusion and delay effects is investigated. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the unique positive steady-state solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition. Our approach to the problem is based on inequality skill and the method of the upper and lower solutions for a more general reaction—diffusion system. Finally, some numerical simulations are given to illustrate our results.http://dx.doi.org/10.1155/2009/317298
collection DOAJ
language English
format Article
sources DOAJ
author Chang-you Wang
Shu Wang
Xiang-ping Yan
spellingShingle Chang-you Wang
Shu Wang
Xiang-ping Yan
Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
Discrete Dynamics in Nature and Society
author_facet Chang-you Wang
Shu Wang
Xiang-ping Yan
author_sort Chang-you Wang
title Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
title_short Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
title_full Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
title_fullStr Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
title_full_unstemmed Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
title_sort global asymptotic stability of 3-species mutualism models with diffusion and delay effects
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2009-01-01
description In this paper, the Lotka-Volterra 3-species mutualism models with diffusion and delay effects is investigated. A simple and easily verifiable condition is given to ensure the global asymptotic stability of the unique positive steady-state solution of the corresponding steady-state problem in a bounded domain with Neumann boundary condition. Our approach to the problem is based on inequality skill and the method of the upper and lower solutions for a more general reaction—diffusion system. Finally, some numerical simulations are given to illustrate our results.
url http://dx.doi.org/10.1155/2009/317298
work_keys_str_mv AT changyouwang globalasymptoticstabilityof3speciesmutualismmodelswithdiffusionanddelayeffects
AT shuwang globalasymptoticstabilityof3speciesmutualismmodelswithdiffusionanddelayeffects
AT xiangpingyan globalasymptoticstabilityof3speciesmutualismmodelswithdiffusionanddelayeffects
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