  We perform a numerical parameter study to determine what effect varying
differential rotation and flux emergence has on a star's non-potential coronal
magnetic field. In particular we consider the effects on the star's surface
magnetic flux, open magnetic flux, mean azimuthal field strength, coronal free
magnetic energy, coronal heating and flux rope eruptions. To do this, we apply
a magnetic flux transport model to describe the photospheric evolution, and
couple this to the non-potential coronal evolution using a magnetofrictional
technique. A flux emergence model is applied to add new magnetic flux onto the
photosphere and into the corona. The parameters of this flux emergence model
are derived from the solar flux emergence profile, however the rate of
emergence can be increased to represent higher flux emergence rates than the
Sun's. Overall we find that flux emergence has a greater effect on the
non-potential coronal properties compared to differential rotation, with all
the aforementioned properties increasing with increasing flux emergence rate.
Although differential rotation has a lesser effect on the overall coronal
properties compared to flux emergence, varying differential rotation does alter
the coronal structure. As the differential rotation rate increases, the corona
becomes more open, and more non-potential.
