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Observations indicate that the star formation rate (SFR) of nuclear rings varies considerably with time and is sometimes asymmetric rather than being uniform across a ring. To understand what controls temporal and spatial distributions of ring star formation, we run semiglobal, hydrodynamic simulations of nuclear rings subject to time-varying and/or asymmetric mass inflow rates. These controlled variations in the inflow lead to variations in the star formation, while the ring orbital period (18 Myr) and radius (600 pc) remain approximately constant. We find that both the mass inflow rate and supernova feedback affect the ring SFR. An oscillating inflow rate with period Δτ_inand amplitude 20 causes large-amplitude (a factor of ≳5), quasi-periodic variations of the SFR when Δτ_in≳ 50 Myr. We find that the time-varying interstellar medium (ISM) weight and midplane pressure track each other closely, establishing an instantaneous vertical equilibrium. The measured time-varying depletion time is consistent with the prediction from self-regulation theory provided the time delay between star formation and supernova feedback is taken into account. The supernova feedback is responsible only for small-amplitude (a factor of ∼2) fluctuations of the SFR with a timescale ≲40 Myr. Asymmetry in the inflow rate does not necessarily lead to asymmetric star formation in nuclear rings. Only when the inflow rate from one dust lane is suddenly increased by a large factor do the rings undergo a transient period of lopsided star formation.