  In this publication we investigate dynamics of a flat FRW cosmological model
with a non-minimally coupled scalar field with the coupling term $\xi R
\psi^{2}$ in the scalar field action. The quadratic potential function
$V(\psi)\propto \psi^{2}$ is assumed. All the evolutional paths are visualized
and classified in the phase plane, at which the parameter of non-minimal
coupling $\xi$ plays the role of a control parameter. The fragility of global
dynamics with respect to changes of the coupling constant is studied in
details. We find that the future big rip singularity appearing in the phantom
scalar field cosmological models can be avoided due to non-minimal coupling
constant effects. We have shown the existence of a finite scale factor singular
point (future or past) where the Hubble function as well as its first
cosmological time derivative diverges.
