Global stability of nonhomogeneous coexisting equilibrium state for the multispecies Lotka–Volterra mutualism models with diffusion

A diffusive multispecies Lotka–Volterra mutualism model is studied in this paper, where the mutualistic interaction coefficients and the diffusion coefficient are spatially heterogeneous. The architecture of these models is one of a hyper-connected central species that interacts with n − 1 peripheral species, but the peripheral species do not interact with each other. By using Lyapunov functional method, the global asymptotic stability of the nonhomogeneous coexisting equilibrium state is established. We extend our results to the multispecies mutualism model in which interaction and diffusion coefficients are spatially homogeneous.