A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation

We study a reaction diffusion system that models the dynamics of two species that display inter-species competition and intra-species cooperation. We find that there are between three and six different equilibrium states and a variety of possible travelling wave solutions that can connect them. After examining the travelling waves that are generated in three different ecologically-relevant initial value problems, we construct asymptotic solutions in the limit λ ≪ 1 (fast diffusion, slow reaction for the second species relative to the first).