Period-doubling events in the light curve of R Cygni: Evidence for chaotic behaviour

L. L. Kiss, K. Szatmáry

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

A detailed analysis of the century long visual light curve of the long-period 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. The next step was to investigate the possible presence of low-dimensional chaos in the light curve. For this, a smoothed and noise-filtered 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 period-doubling 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 ∼1500-day 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 third-order differential equation which exhibits well-expressed period-doubling 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.

Original languageEnglish
Pages (from-to)585-596
Number of pages12
JournalAstronomy and Astrophysics
Volume390
Issue number2
Publication statusPublished - Aug 2002

Fingerprint

period doubling
light curve
chaotic dynamics
bifurcation
embedding
chaos
exponents
Fourier analysis
frequency analysis
periodicity
periodic variations
differential equations
time lag
switches
diagram
diagrams
orbits
stars
approximation

Keywords

  • Stars: AGB and post-AGB
  • Stars: individual: R Cygni
  • Stars: late-type
  • Stars: variables: general

ASJC Scopus subject areas

  • Space and Planetary Science

Cite this

Period-doubling events in the light curve of R Cygni : Evidence for chaotic behaviour. / Kiss, L. L.; Szatmáry, K.

In: Astronomy and Astrophysics, Vol. 390, No. 2, 08.2002, p. 585-596.

Research output: Contribution to journalArticle

@article{4d26106290344b79847ec2f77d2ee659,
title = "Period-doubling 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 long-period 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. The next step was to investigate the possible presence of low-dimensional chaos in the light curve. For this, a smoothed and noise-filtered 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 period-doubling 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 ∼1500-day 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 third-order differential equation which exhibits well-expressed period-doubling 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.",
keywords = "Stars: AGB and post-AGB, Stars: individual: R Cygni, Stars: late-type, Stars: variables: general",
author = "Kiss, {L. L.} and K. Szatm{\'a}ry",
year = "2002",
month = "8",
language = "English",
volume = "390",
pages = "585--596",
journal = "Astronomy and Astrophysics",
issn = "0004-6361",
publisher = "EDP Sciences",
number = "2",

}

TY - JOUR

T1 - Period-doubling events in the light curve of R Cygni

T2 - Evidence for chaotic behaviour

AU - Kiss, L. L.

AU - Szatmáry, K.

PY - 2002/8

Y1 - 2002/8

N2 - A detailed analysis of the century long visual light curve of the long-period 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. The next step was to investigate the possible presence of low-dimensional chaos in the light curve. For this, a smoothed and noise-filtered 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 period-doubling 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 ∼1500-day 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 third-order differential equation which exhibits well-expressed period-doubling 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.

AB - A detailed analysis of the century long visual light curve of the long-period 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. The next step was to investigate the possible presence of low-dimensional chaos in the light curve. For this, a smoothed and noise-filtered 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 period-doubling 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 ∼1500-day 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 third-order differential equation which exhibits well-expressed period-doubling 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.

KW - Stars: AGB and post-AGB

KW - Stars: individual: R Cygni

KW - Stars: late-type

KW - Stars: variables: general

UR - http://www.scopus.com/inward/record.url?scp=0036682351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036682351&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036682351

VL - 390

SP - 585

EP - 596

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

IS - 2

ER -