  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 the
initial metallicity $Z=0.014$. Selected models of evolutionary sequences with
envelopes under thermal equilibrium were used as initial conditions for
calculation of nonlinear stellar pulsations. The hydrodynamic models of each
evolutionary sequence are shown to concentrate along the continuous line in the
period-radius and period-luminosity diagrams. The theoretical period-radius and
period-luminosity relations differ from one another for different main-sequence
star masses because the stellar luminosity of AGB stars depends on the
degenerate 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 $174~\textrm{d}\le\Pi\le
204~\textrm{d}$, whereas all models of the evolutionary sequence
$M_\mathrm{ZAMS}=1.5M_\odot$ oscillate in the fundamental mode. Fairly regular
radial 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.

Solar and Stellar Astrophysics