Abstract
In this publication we investigate dynamics of a flat FRW cosmological modelwith a non-minimally coupled scalar field with the coupling term ξRψ2 in the scalar field action. The quadratic potential functionV(ψ) ∝ ψ2 is assumed. All the evolutional paths are visualizedand classified in the phase plane, at which the parameter of non-minimalcoupling ξ plays the role of a control parameter. The fragility of globaldynamics with respect to changes of the coupling constant is studied in details.We find that the future big rip singularity appearing in the phantom scalarfield cosmological models can be avoided due to non-minimal coupling constanteffects. We have shown theexistence of a finite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverge.
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