A detailed analysis of the century long visual light curve of the Mira star R Cygni is presented and discussed. The data were collected from the publicly available databases of the AFOEV, the BAAVSS and the VSOLJ. The full light curve consists of 26655 individual points obtained between 1901 and 2001. The light curve and its periodicity were analysed with help of the O-C diagram, Fourier analysis and time-frequency analysis. The results demonstrate the limitations of these linear methods. A smoothed and noise filtered signal was created from the averaged data and with help of time delay embedding, we have tried to reconstruct the attractor of the system. The main result is that R Cygni shows such period-doubling events that can be interpreted as caused by a repetitive bifurcation of the chaotic attractor between a period 2T orbit and chaos. The switch between these two states occurs in a certain compact region of the phase space, where the light curve is characterized by 1500-days long transients. The light curve is compared with a simple one zone model generated by a third-order differential equation which exhibits well-expressed period doubling bifurcation. The strong resemblance is another argument for chaotic behaviour. This is the first case of positive detection of chaotic pulsation in a Mira star thus allowing the extension of non-linear asteroseismology (being still in its infancy) toward this class of pulsating stars.

 
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