Let x and y denote the biomass of two species respectively. (Biomass simply means the total quantity or weight of an organism in a given area.) Assume that the two species compete for food, so that the rate of growth of each species is negatively related to the biomass of the other species. Suppose functional forms showing evolution of x and y are:
i) Find all the possible intertemporal equilibria.
ii) Using a phase diagrammatic technique, discuss the stability/instability of the interior equilibrium. (Note: For full marks, all trajectories must clearly be marked and the mathematical derivation shown and explained in some detail. Poorly drawn diagrams will be penalized.)