A reaction diffusion model for competing pioneer and climax species

Presented is a reaction-diffusion model for the interaction of a pioneer and climax species. The linear stability analysis of the kinetic equilibria are examined and the existence of a Hopf bifurcation is shown. A specific model is used to demonstrate the dynamics of the system. Diffusion is introduced into the kinetic system to model the spatial dispersion of the species. An analysis for the existence of a Turing bifurcation is performed. Again a specific model is examined for the possibility of Turing bifurcations and bifurcation diagrams are produced. Finally traveling wave solutions for the full reaction-diffusion system are examined. It is found using geometric singular perturbation theory that there exists a traveling wave solution to the system with wave speed of Oe.