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.
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