  For a group of the Mira-type stars, semi-regular variables and some RV Tau -
type stars the limit cycles were computed and plotted using the phase plane
diagrams. As generalized coordinates x and $\dot{x},$ we have used $\phi$ - the
brightness of the star and its phase derivative. We have used mean phase light
curves using observations of various authors from the databases of AAVSO,
AFOEV, VSOLJ, ASAS and approximated using a trigonometric polynomial of
statistically optimal degree. As generalized coordinates x and $\dot{x}$, we
have used m - the brightness of the star and its phase derivative. For a simple
sine-like light curve, the limit cycle is a simple ellipse. In a case of more
complicated light curve, in which harmonics are statistically significant, the
limit cycle has deviations from the ellipse. In an addition to a classical
analysis, we use the error estimates of the smoothing function and its
derivative to constrain an "error corridor" in the phase plane.
