A diffusive two predators–one prey model on periodically evolving domains

The paper deals with a diffusive two predators–one prey model with Holling-type II functional response. We assume that the density of prey and predators is spatially inhomogeneous on a periodically evolving domain and is subject to homogeneous Neumann boundary conditions. We focus on the case in which all populations have periodic logistic growth, if isolated, and no competition occurs between predators. Our main purpose is to study the asymptotic properties of the solutions of this reaction–diffusion model. More specifically, suitable conditions, depending on the domain evolution function and the space dimension, are introduced leading to the extinction of one predator and the stable coexistence of the surviving predator and its prey. Their density, as time tends to infinity, tends to the periodic solution of the corresponding kinetic predator–prey model. Finally, the autonomous model on a fixed domain is treated.