  Overcontact binary stars are systems of two stars where the component stars
are in contact with each other. This implies that they share a common envelope
of gas. In this work we seek signatures of nonlinearity and chaos in these
stars by using time series analysis techniques. We use three main techniques,
namely the correlation dimension,f (\alpha) spectrum and the bicoherence. The
former two are calculated from the reconstructed dynamics, while the latter is
calculated from the Fourier transforms of the time series of intensity
variations(light curves) of these stars. Our dataset consists of data from 463
overcontact binary stars in the Kepler field of view [1]. Our analysis
indicates nonlinearity and signatures of chaos in almost all the light curves.
We also explore whether the underlying nonlinear properties of the stars are
related to their physical properties like fill-out-factor, a measure of the
extend of contact between the components of an overcontact binary system . We
observe that significant correlations exist between the fill out factor and the
nonlinear quantifiers. This correlation is more pronounced in specific
subcategories constructed based on the mass ratios and effective temperatures
of the binaries. The correlations observed can be indicative of variations in
the nonlinear properties of the star as it ages. We believe that this study
relating nonlinear and astrophysical properties of binary stars is the first of
its kind and is an important starting point for such studies in other
astrophysical objects displaying nonlinear dynamical behaviour.
