Biological control of parasites on orange plantations : a predator prey model

Abstract

In this thesis, a four dimensional autonomous dynamical system, proposed as a model for biological control of a parasite on citrus plantations, is studied. The model is the same as that studied by Sotomayor et. al. in [1], where the system is found to have four equilibrium points, of which one exhibits a Hopf bifurcation, and a bifurcation curve is found.

In this thesis, we review and complement the work of Sotomayor et. al. [1], by proving the existence of an invariant set (volume) in the first orthant, though not for proposed parameter values. Furthermore the set is shown to be dissipative, that is, the phase fluids inside the invariant set is contracted to one of measure zero.

Then the dynamics of the normal form is compared numerically to those of the full system near the bifurcation point, for fixed parameter values