Egg-eating predators in interaction with age-structured prey population

Abstract

We investigate a predator-prey model for egg-eating predators in which the prey population is assumed to have an age structure. By the method of characteristics, this model reduces to a system of integral equations. Then a generalization of the Banach fixed-point theorem is used to show, under relatively mild conditions, the existence of a unique, global, weak solution to the population problem. Furthermore, this methodology allows us to generate a sequence of iterates, called the Picard iterates, that converges to the solution. Also, we strengthen the assumptions of the existence-uniqueness theorem to establish the validity of the corresponding conservation law in integral form. Thus we prove a result which shows the coexistence of both predator and prey species over a long time.