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Pulsation period decrease during the initial stage of the thermal pulse inthe helium-burning shell of the Mira-type variable T UMi is investigated withnumerical methods of stellar evolution and radiation hydrodynamics. To thisend, a grid of evolutionary tracks was calculated for stars with masses on themain sequence $1M_\odot\le M_\textrm{ZAMS}\le 2.2M_\odot$ and metallicity$Z=0.01$. Selected models of AGB evolutionary sequences were used fordetermination of the initial conditions and the time--dependent inner boundaryconditions for the equations of hydrodynamics describing evolutionary changesin the radially pulsating star. The onset of period decrease during the initialstage of the thermal pulse is shown to nearly coincide with the peakhelium-burning luminosity. The most rapid decrease of the period occurs duringthe first three decades. The pulsation period decreases due to both contractionof the star and mode switching from the fundamental mode to the first overtone.The time-scale of mode switching is of the order of a few dozen pulsationcycles. The present-day model of the Mira-type variable T UMi is thefirst-overtone pulsator with small-amplitude semi-regular oscillations.Theoretical estimates of the pulsation period at the onset of period decreaseand the rate of period change three decades later are shown to agree withavailable observational data on T UMi for AGB stars with masses $1.04M_\odot\le M\le 1.48M_\odot$.

Hydrodynamic modelling of pulsation period decrease in the Mira-type variable T UMi