We present hydrodynamic BL Herculis type models which display a long-term modulation of pulsation amplitudes and phases. The modulation is either strictly periodic or quasi-periodic, with the modulation period and modulation pattern varying from one cycle to another. Such behaviour has not been observed in any BL Herculis variable so far; however, it is a common property of their lower luminosity siblings – RR Lyrae variables showing the Blazhko effect. These models provide support for the recent mechanism proposed by Buchler & Kolláth to explain this still mysterious phenomenon. In their model, a half-integer resonance that causes the period-doubling effect, discovered recently in Blazhko RR Lyrae stars, is responsible for the modulation of pulsation as well. Although our models are more luminous than is appropriate for RR Lyrae stars, they clearly demonstrate, through direct hydrodynamic computation, that the mechanism can indeed be operational.
Of great importance are models that show quasi-periodic modulation – a phenomenon observed in Blazhko RR Lyrae stars. Our models coupled with the analysis of the amplitude equations show that such behaviour may be caused by the dynamical evolution occurring in the close proximity of the unstable single periodic saddle point.