Optimal Foraging and Predator-Prey Dynamics

A system consisting of a population of predators and two types of prey is considered. The dynamics of the system is described by differential equations with controls. The controls model how predators forage on each of the two types of prey. The choice of these controls is based on the standard assumption in the theory of optimal foraging which requires that each predator maximizes the net rate of energy intake during foraging. Since this choice depends on the densities of populations involved, this allows us to link the optimal behavior of an individual with the dynamics of the whole system. Simple qualitative analysis and some simulations show the qualitative behavior of such a system. The effect of the optimal diet choice on the stability of the system is discussed.