Singular Perturbation Approach to a 3-component Reaction-Diffusion System Arising in Population Dynamics

In order to understand theoretically predation-mediated coexistence of competing species which is often observed in ecological systems, we consider a 3-component reaction-diffusion system describing the interaction of one predator and two competing prey species which move by diffusion. It is shown that there exist stable spatially inhomogeneous positive equilibrium solutions of the one-dimensional system under the Neumann boundary condition. This implies ecologically that in the presence of the predator, two competing species coexist with spatially segregating structures. The main tools we use are the singular perturbation technique and the associated singular limit spectral analysis.