  Nuclear rings in barred galaxies are sites of active star formation. We use
hydrodynamic simulations to study temporal and spatial behavior of star
formation occurring in nuclear rings of barred galaxies where radial gas
inflows are triggered solely by a bar potential. The star formation recipes
include a density threshold, an efficiency, conversion of gas to star
particles, and delayed momentum feedback via supernova explosions. We find that
star formation rate (SFR) in a nuclear ring is roughly equal to the mass inflow
rate to the ring, while it has a weak dependence on the total gas mass in the
ring. The SFR typically exhibits a strong primary burst followed by weak
secondary bursts before declining to very small values. The primary burst is
associated with the rapid gas infall to the ring due to the bar growth, while
the secondary bursts are caused by re-infall of the ejected gas from the
primary burst. While star formation in observed rings persists episodically
over a few Gyr, the duration of active star formation in our models lasts for
only about a half of the bar growth time, suggesting that the bar potential
alone is unlikely responsible for gas supply to the rings. When the SFR is low,
most star formation occurs at the contact points between the ring and the dust
lanes, leading to an azimuthal age gradient of young star clusters. When the
SFR is large, on the other hand, star formation is randomly distributed over
the whole circumference of the ring, resulting in no apparent azimuthal age
gradient. Since the ring shrinks in size with time, star clusters also exhibit
a radial age gradient, with younger clusters found closer to the ring. The
cluster mass function is well described by a power law, with a slope depending
on the SFR. Giant gas clouds in the rings have supersonic internal velocity
dispersions and are gravitationally bound.
