A Reaction-Diffusion Model For Competing Between Two Species

This study deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system a natural extension of the Lotka-Volterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions with four regions in which the solutions are similar to those in the Lotka-Volterra system. We study RDS in the small parameter of the range 0