An Investigation of the Effects of Diffusion on a Competition Model

We present a reaction-diffusion competition model, to describethe spatial spread of two competing species. Standard analysisof the model using the travelling wave procedure was employedto determine the existence of travelling wave solutions andthe stability of the equilibrium points. The result shows thatthe zero equilibrium point is stable, contrary to that of adiffusion-free competition model. The result is further confirmed using the normal modes analysis. This result is however,more general than the special case considered by Okubo, et al(1989). The remaining three steady states are saddle points,thus guaranteeing the existence of travelling wave solutions inform of heteroclinic connections among the equilibrium points.