  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 work, 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 the attention on certain
solutions that reproduce with reasonable accuracy the observed behaviour of
some peculiar Mira variables.
