overtone and the fundamental mode is visibly lower than in Model1 and has a value $P_2/P_1 \simeq 0.74$. In Model2, the radial orders of pulsation modes are much larger,in particular for the quadruple mode. For the considered range of $\nu$, cf. Fig.\[fig4\], the values of $n$ are: $(60,1400)$ for $\ell=1$ and $(100,2400)$ for $\ell=2$.

In Fig.\[fig5\], we compare the kinetic energy densities, $E_k$ (top panels), and differential work integrals, $\mathrm{d}W/\mathrm{d}\log T$ (bottom panels), for unstable and stable modes of the degree $\ell=2$ with very close frequencies. The left group of panels is for Model1 (before core helium ignition) and the left group of panels for Model2 (after core helium ignition). The behaviour of presented modes is typical and representative for all unstable and stable modes during shell hydrogen burning and on the blue loops. The properties of pulsational modes in the shell hydrogen burning model have been already presented in D2013 but for comparative purposes we repeat them here.

In Model1, both unstable ($\nu=0.301$ c/d, $\eta=0.093$) and stable ($\nu=0.296~d^{-1}$, $\eta=-0.983$) modes exhibit a very strong damping in the radiative helium core, which is visible in the behaviour of $\mathrm{d}W/\mathrm{d}\log T$ in the bottom panels of the left group. As shown 