Spatial pattern formation for steady states of a population model

Abstract

In this paper some exact solutions are presented for the steady states of a two-component diffusion model with a one-dimensional spatial structure. The interaction terms are based on those posed for population models with competing species. The same equations arise in many other situations in, for example, chemistry and physics. This generic model, which is the simplest nonlinear model that is odd in the dependent variables, has a complex solution set which is determined by exact and asymptotic analysis of the equations. The bifurcation diagram exhibits multiple branching after a threshold value of the diffusion coefficients is reached. In the limit of low diffusion of the species, limiting forms of the solutions can be found. No periodic solutions are possible for this model.

Spatial structure, stability, competition, squirrels