Archimedean-type force in a cosmic dark fluid: II. Qualitative and
  numerical study of a multistage Universe expansion
  In this (second) part of the work we present the results of numerical and
qualitative analysis, based on a new model of the Archimedean-type interaction
between dark matter and dark energy. The Archimedean-type force is linear in
the four-gradient of the dark energy pressure and plays a role of
self-regulator of the energy redistribution in a cosmic dark fluid. Because of
the Archimedean-type interaction the cosmological evolution is shown to have a
multistage character. Depending on the choice of the values of the model
guiding parameters,the Universe's expansion is shown to be perpetually
accelerated, periodic or quasiperiodic with finite number of
deceleration/acceleration epochs. We distinguished the models, which can be
definitely characterized by the inflation in the early Universe, by the
late-time accelerated expansion and nonsingular behavior in intermediate
epochs, and classified them with respect to a number of transition points.
Transition points appear, when the acceleration parameter changes the sign,
providing the natural partition of the Universe's history into epochs of
accelerated and decelerated expansion. The strategy and results of numerical
calculations are advocated by the qualitative analysis of the instantaneous
phase portraits of the dynamic system associated with the key equation for the
dark energy pressure evolution.
