R Centauri has long been identified as a peculiar Mira variable showing prominent double maxima. The star reaches a local maximum -- one slightly fainter than the other -- with each pulsation cycle of around 550 days. The physical cause of this isn't clear, but one possibility is the presence of a period resonance between two of the radial modes. A mode is one of an infinite number of possible vibration states of a system. Most Mira variables pulsate in the radial fundamental mode, meaning (a) the star is pulsating radially, in spherical symmetry, and (b) the entire star is pulsating in and out, and the only fixed point is the center of the star. A radial first overtone mode would also be radially pulsating, but there would be a node (in this case, a spherical shell) within the star which doesn't move. Each of these modes has its own pulsation period, and sometimes the periods of the overtone modes can be an integer fraction of the fundamental mode, leading to a resonance.
R Cen also has another peculiarity -- it's period is known to have changed during the past century. Again, the reason isn't known for sure, but it's possible that the interior structure of the star may be changing due to a thermal pulse, where a shell of helium deep within the core undergoes very rapid nuclear burning from helium to carbon, releasing heat and changing the equilibrium structure as a result. One result of this process is a change in period, and its possible that the change in the shape of R Cen's light curve over time reflects this. If the periods of the modes responsible for the resonance change, so does the stability of the resonance.