Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 317298, 20 pages
Global Asymptotic Stability of 3-Species Mutualism Models with Diffusion and Delay Effects
1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network control & Intelligent Instrument, (Chongqing University of Posts and Telecommunications), Ministry of Education, Chongqing 400065, China
3College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
4Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
Received 21 March 2009; Accepted 6 June 2009
Academic Editor: Leonid Berezansky
Copyright © 2009 Chang-you Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.