HOPF BIFURCATION IN PREDATOR-PREY MODELS WITH AN AGE-STRUCTURED PREY PROCEEDINGS

摘要

In this paper is analyzed the existence of periodic orbits in a predator-prey interaction, when the predator feeds on each one of the two age classes of the prey. Three families of models are considered in correspondence with different prey and predator behaviors. Specifically, a constant predation rate on the non reproductive class of the prey is considered in the first family; a Holling predation of type two on the non reproductive class is incorporated in the second and in the third family; a defense group mechanism of the reproductive class is introduced in the third family. We prove that these three families of models exhibit Hopf bifurcations and the Hopf periodic orbit is a local attractor.