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 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.