  We have used the dynamical system approach in order to investigate the
dynamics of cosmological models of the flat Universe with a non-minimally
coupled canonical and phantom scalar field and the Ratra-Peebles potential.
Applying methods of the bifurcation theory we have found three cases for which
the Universe undergoes a generic evolution emerging from either the deSitter or
the static Universe state and finishing at the deSitter state, without the
presence of the initial singularity. This generic class of solutions explains
both the inflation and the late-time acceleration of the Universe. In this
class inflation is an endogenous effect of dynamics itself.
