Existence and Instability of Neumann Layer Solutions for a 3-component Lotka–Volterra Model with Diffusion

We consider a 3-component Lotka–Volterra model with diffusion which describes the dynamics of the population of two competing prey and one predator, and we discuss the existence of positive stationary solutions and their stability property. To do this, the singular perturbation method and the associated singular limit spectral analysis are employed.