A weakly non-adiabatic one-zone model of stellar pulsations:: application to Mira stars

There is growing observational evidence that the irregular changes in the light curves of certain variable stars might be due to deterministic chaos. Supporting these conclusions, several simple models of non-linear oscillators have been shown to be capable of reproducing the observed complex behaviour. In this paper, we introduce a non-linear, non-adiabatic one-zone model intended to reveal the factors leading to irregular luminosity variations in some pulsating stars. We have studied and characterized the dynamical behaviour of the oscillator as the input parameters are varied. The parametric study implied values corresponding to stellar models in the family of long period variables and in particular of Mira-type stars. We draw attention to certain solutions that reproduce with reasonable accuracy the observed behaviour of some peculiar Mira variables.