We investigate the theoretical scenario concerning the large sample of variables recently discovered in the dwarf, metal-poor irregular galaxy Leo A, focusing the attention on the Anomalous Cepheid phenomenon and its correlation with RR Lyrae stars, Classical and Population II Cepheids. To this purpose, we make use of suitable stellar and pulsation models to depict the pulsational history of evolutionary structures with metallicity Z=0.0004, finding that He-burning pulsators are expected only outside the mass interval ~ 0.8-1.7 Mo. The dependence on metal content of this scenario has been investigated over the range Z=0.0002 to 0.008. One finds that the edges of the pulsational strip for the more massive class of pulsators appear independent of metallicity, but with the minimum mass of these bright pulsators which decreases when decreasing the metallicity, thus decreasing the predicted minimum luminosity and period. Comparison with data for Cepheids in Leo A and in the moderately metal rich extragalactic stellar system Sextans A discloses an encouraging agreement with the predicted pulsational scenario. On this basis, we predict that in a stellar system where both RR Lyrae stars and Cepheids are observed, their magnitude difference may help in constraining both the metal content and the distance. The current classification of metal-poor Cepheids is shortly discussed, advancing the suggestion for an updated terminology abreast of the current knowledge of stellar evolution.
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