  In this paper, we model the bounce phase, stability and the reconstruction of
the universe by non-minimal kinetic coupling. In the process, we obtained
importance information about the energy density and the matter pressure of the
universe in relation to the previous universe through the bounce quantum phase.
The novelty of the work is that the scale factor is obtained directly from the
model and is fitted with an exponential function, with this view we explore the
process of the early universe even the bounce phase. After that, we plot the
cosmological parameters in terms of time evolution. In what follows, we
investigate the stability of the model by the dynamical system analysis in a
phase plane. Finally, we examine the stability of the universe, especially in
the inflationary period, by using the phase space trajectories.
