Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 317298, 20 pages
doi:10.1155/2009/317298
Global asymptotic stability of 3-species mutualism models with diffusion and delay effects
Chang-You Wang1
, Shu Wang2
and Xiang-Ping Yan3
1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
3Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
Abstract
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.