A 3-component system of competition and diffusion

This report studies the existence of non-constant solutions of certain two-point boundary value problems for 3-component systems with a small parameter epsilon, under homogeneous Neumann conditions at the boundaries. This problem is related to the analysis of segregation patterns in population models of 3-competing and spatially dispersing species. It is shown that the reduced problem (epsilon = 0) has many non-constant solutions exhibiting spatial segregation. Only a few of these, however, can serve as valid lowest-order approximations to solutions of the original problem when epsilon is non-zero but small. A singular perturbation construction clarifies which are in this category. The results of numerical computations of solutions are also illustrated. (Author)