  The main difficulties in constructing a viable early Universe bouncing model
are: to bypass the observational and theoretical \emph{no-go} theorem, to
construct a stable non-singular bouncing phase and perhaps, the major concern
of it is to construct a stable attractor solution which can evade the BKL
instability as well. In this article, in the homogeneous and isotropic
background, we extensively study the stability analysis of the recently
announced viable non-minimal bouncing theory in the presence of an additional
barotropic fluid and show that, the bouncing solution remains stable and can
evade BKL instability for a wide range of the model parameter. We provide the
expressions that explain the behavior of the Universe in the vicinity of the
required fixed point i.e., the bouncing solution and compare our results with
the minimal theory and show that ekpyrosis is the most stable solution in any
scenario.
