Perioddoubling events in the light curve of R Cygni: Evidence for chaotic behaviour
Abstract
A detailed analysis of the century long visual light curve of the longperiod 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 OC diagram, Fourier analysis and timefrequency analysis. The results demonstrate the limitations of these linear methods. The next step was to investigate the possible presence of lowdimensional chaos in the light curve. For this, a smoothed and noisefiltered signal was created from the averaged data and with the help of time delay embedding, we have tried to reconstruct the attractor of the system. The main result is that R Cygni shows such perioddoubling events that can be interpreted as being 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 ~ 1500day long transients. The Lyapunov spectrum was computed for various embedding parameters confirming the chaotic attractor, although the exponents suffer from quite high uncertainty because of the applied approximation. Finally, the light curve is compared with a simple one zone model generated by a thirdorder differential equation which exhibits wellexpressed perioddoubling bifurcation. The strong resemblance is another argument for chaotic behaviour. Further studies should address the problem of global flow reconstruction, including the determination of the accurate Lyapunov exponents and dimension.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 August 2002
 DOI:
 10.1051/00046361:20020744
 arXiv:
 arXiv:astroph/0205334
 Bibcode:
 2002A&A...390..585K
 Keywords:

 stars: variables: general;
 stars: latetype;
 stars: AGB and postAGB;
 stars: individual: R Cygni;
 Astrophysics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 13 pages, 14 figures, accepted for publication in A&