Lava dome eruptions commonly display fairly regular alternations between periods of high and low or no activity with timescales typically of weeks to years and sudden transitions between effusive and explosive activity. We develop a transient model of the magma flow in a volcanic conduit from an open-system magma chamber with continuous replenishment. The model incorporates gas exsolution, bubble growth, gas escape through the magma, and decompression-induced crystallization and considers variations in magma temperature, water content, conduit diameter, phenocryst size, chamber volume, and magma rheology. Calculations show the presence of periodic variations in discharge rate due to the transition from a stable regime, when discharge rate is low and crystals grow efficiently leading to high magma viscosity, to another stable state, when discharge rate is high and crystallization is negligible. The difference in discharge rates between these regimes can be several orders of magnitude. Periods are similar to the observed timescales and mainly depend on the chamber volume. The system shows strongly nonlinear responses to the variation of governing parameters. If magma has a Bingham rheology pauses in discharge rate occur between peaks of discharge and the peaks are much higher than for the case of Newtonian rheology. Large changes in discharge rate and eruptive behavior can occur as the consequence of small changes in magma temperature, water content, phenocryst size distribution, or conduit diameter. The system can fluctuate between low and high discharge rates with transitions to explosive activity.