  To understand star formation in galaxies, we investigate the star formation
rate (SFR) surface density ($\Sigma_{\rm SFR}$) profiles for galaxies, based on
a well-defined sample of 976 star-forming MaNGA galaxies. We find that the
typical $\Sigma_{\rm SFR}$ profiles within 1.5Re of normal SF galaxies can be
well described by an exponential function for different stellar mass intervals,
while the sSFR profile shows positive gradients, especially for more massive SF
galaxies. This is due to the more pronounced central cores or bulges rather
than the onset of a `quenching' process. While galaxies that lie significantly
above (or below) the star formation main sequence (SFMS) show overall an
elevation (or suppression) of $\Sigma_{\rm SFR}$ at all radii, this central
elevation (or suppression) is more pronounced in more massive galaxies. The
degree of central enhancement and suppression is quite symmetric, suggesting
that both the elevation and suppression of star formation are following the
same physical processes. Furthermore, we find that the dispersion in
$\Sigma_{\rm SFR}$ within and across the population is found to be tightly
correlated with the inferred gas depletion time, whether based on the stellar
surface mass density or the orbital dynamical time. This suggests that we are
seeing the response of a simple gas-regulator system to variations in the
accretion rate. This is explored using a heuristic model that can
quantitatively explain the dependence of $\sigma(\Sigma_{\rm SFR})$ on gas
depletion timescale. Variations in accretion rate are progressively more damped
out in regions of low star-formation efficiency leading to a reduced amplitude
of variations in star-formation.
