A reaction diffusion model for inter-species competition and intra-species cooperation (Q2843429)

This paper deals with a reaction-diffusion spatially structured model for a system of two species that compete for resources and cooperate within each species. It is shown that there are always three equilibria belonging to the boundary of the spatial domain and at most another three positive equilibria, corresponding to coexisting solutions. Also, travelling wave solutions connecting these equilibria are examined. Choosing ecologically relevant initial data, numerical simulations show that these travelling waves exist and asymptotic solutions in the case of fast diffusion and slow reaction for the second species relative to the first are numerically constructed.