  The gravitating Julia-Zee dyon is a particle-like solution with both electric
and magnetic charge. It is found in the Einstein-Yang-Mills-Higgs system of
SU(2) with a scalar field in the adjoint representation coupled to gravity.
Within the magnetic ansatz this system is reduced from describing dyons to
describing the gravitating 't Hooft-Polyakov magnetic monopole. The stability
of the well-known static gravitating magnetic monopole solutions with respect
to perturbations within the magnetic ansatz--so-called magnetic
perturbations--is well studied, but their stability with respect to
perturbations outside the magnetic ansatz--so-called sphaleronic
perturbations--is not. I undertake a purely numerical study by adding
sphaleronic perturbations to gravitating magnetic monopole solutions and then
dynamically evolving the system. For large perturbations I find that the system
heads toward a dyon configuration, as expected. For sufficiently small
perturbations, however, the system oscillates about the magnetic ansatz in a
manner consistent with oscillations about a stable equilibrium.
