  We explore the regulation of star formation in star-forming galaxies through
a suite of high-resolution isolated galaxy simulations. We use the SPH code
GASOLINE, including photoelectric heating and metal cooling, which produces a
multi-phase interstellar medium. We show that representative star formation and
feedback sub-grid models naturally lead to a weak, sub-linear dependence
between the amount of star formation and changes to star formation parameters.
We incorporate these sub-grid models into an equilibrium pressure-driven
regulation framework. We show that the sub-linear scaling arises as a
consequence of the non-linear relationship between scale height and the
effective pressure generated by stellar feedback. Thus, simulated
star-formation regulation is sensitive to how well vertical structure in the
ISM is resolved. Full galaxy disks experience density waves which drive locally
time-dependent star formation. We develop a simple time-dependent,
pressure-driven model that reproduces the response extremely well.
