Self-regulation and resource dependent growth rates: A size-structured predator-prey model

The dynamical behavior of a size-structured predator-prey model with nonlinear growth rates is studied. In the model prey growth rate decreases with prey population density, while predator growth rate depends on predation. Existence and uniqueness of solutions are proved under weak conditions. A threshold is established for the stability of the predator-free equilibrium and the existence of a positive equilibrium. When restricted only to the prey, the model is a special case of the one studied by Farkas and Hagen [13]; in this case it is shown that the positive equilibrium may undergo Hopf bifurcation, a novel feature in this class of models.