| dc.description.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 | nb_NO |
