  In the centres of the Milky Way and M83, the global environmental properties
thought to control star formation are very similar. However, M83's nuclear star
formation rate (SFR), as estimated by synchrotron and H-alpha emission, is an
order of magnitude higher than the Milky Way's. To understand the origin of
this difference we use ALMA observations of HCN (1-0) and HCO+ (1-0) to trace
the dense gas at the size scale of individual molecular clouds (0.54", 12pc) in
the inner ~500 pc of M83, and compare this to gas clouds at similar resolution
and galactocentric radius in the Milky Way. We find that both the overall gas
distribution and the properties of individual clouds are very similar in the
two galaxies, and that a common mechanism may be responsible for instigating
star formation in both circumnuclear rings. Given the considerable similarity
in gas properties, the most likely explanation for the order of magnitude
difference in SFR is time variability, with the Central Molecular Zone (CMZ)
currently being at a more quiescent phase of its star formation cycle. We show
M83's SFR must have been an order of magnitude higher 5-7 Myr ago. M83's
`starburst' phase was highly localised, both spatially and temporally, greatly
increasing the feedback efficiency and ability to drive galactic-scale
outflows. This highly dynamic nature of star formation and feedback cycles in
galaxy centres means (i) modeling and interpreting observations must avoid
averaging over large spatial areas or timescales, and (ii) understanding the
multi-scale processes controlling these cycles requires comparing snapshots of
a statistical sample of galaxies in different evolutionary stages.
