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Evolutionary sequences of AGB stars with initial masses on the main sequence$M_\mathrm{ZAMS}=1.5M_\odot$, $2M_\odot$ and $3M_\odot$ were computed for theinitial metallicity $Z=0.014$. Selected models of evolutionary sequences withenvelopes under thermal equilibrium were used as initial conditions forcalculation of nonlinear stellar pulsations. The hydrodynamic models of eachevolutionary sequence are shown to concentrate along the continuous line in theperiod-radius and period-luminosity diagrams. The theoretical period-radius andperiod-luminosity relations differ from one another for different main-sequencestar masses because the stellar luminosity of AGB stars depends on thedegenerate carbon core mass which increases with increasing $M_\mathrm{ZAMS}$.In hydrodynamic models of evolutionary sequences $M_\mathrm{ZAMS}=2M_\odot$ and$M_\mathrm{ZAMS}=3M_\odot$ the periods of the first overtone pulsators are$86~\textrm{d}\le\Pi\le 123~\textrm{d}$ and $174~\textrm{d}\le\Pi\le204~\textrm{d}$, whereas all models of the evolutionary sequence$M_\mathrm{ZAMS}=1.5M_\odot$ oscillate in the fundamental mode. Fairly regularradial oscillations exist in stars with pulsation periods $\Pi\lesssim 500$ d.In models with longer periods the amplitude rapidly increases with increasing$\Pi$ and oscillations become irregular.

Theoretical period-radius and period-luminosity relations for Mira variables with solar metallicity