A SEARCH FOR CHAOTIC BEHAVIOR IN THE LIGHT CURVES OF 3 LONG-PERIOD VARIABLES

We present the results of a study of the light curves taken by the American Association of Variable Star Observers of the long-period variables o Ceti (Mira), R Leonis, and V Bootis. In searching for evidence of deterministic chaos, we employ the technique of Grassberger and Procaccia in which the dimension of an attractor can in principle be inferred from a long time series of physical measurements of a system. We also compute autocorrelation functions and power spectra. The variations seen in the optical light are basically periodic, with P∼ 332 days (Mira), 313 days (R Leo), and 259 days (V Boo). The power spectra exhibit maxima at frequencies corresponding to these times, and harmonics are observed up to order 3 or 4. The variations in the light curves can be modeled by adding two components, one periodic and one random. A good simulation of the light curves is obtained if the amplitude of the random variations is about one-half that of the periodic amplitude.