A diffusive intraguild predation model with variable-carrying capacity proportional to the same biotic resource

In this paper, we investigate the initial-boundary value problem of a diffusive three-species intraguild predation model, in which the variable-carrying capacity is proportional to the biotic resource and the biotic resource follows the logistic law. We mainly discuss the stabilities of the constant equilibrium points at different levels of enrichment, including the linear local, global stability and nonlinear stability. Finally, the non-existence of non-constant positive steady states has been shown.