R Normae is another famous Mira exhibiting the peculiar phenomenon of double maxima -- two bright maxima per pulsation cycle. The reason for this behavior isn't known for certain, but two possibilities are (a) resonances between two pulsation modes, or (b) the formation of shocks in their atmospheres during the pulsation cycle. The other stars like R Normae, including R Centauri, have long periods, and it's possible that their behavior is related to what's going on in their extended atmospheres during the pulsation cycle. Because of the long periods, the atmosphere reflects the pulsation wave back into the star, potentially reinforcing it and generating a second shock, which we would see as a second bright peak in the light curve. Scenarios for this behavior were discussed by Templeton and Willson (2005), and are the subject of one of the research projects of the AAVSO LPV Section.