  We study the dynamics of expansion of the homogeneous isotropic Universe and
the evolution of its components in the model with nonminimally coupled
dynamical dark energy. Dark energy, like the other components of the Universe,
is described by the perfect fluid approximation with the equation of state
(EoS) $p_ {de}=w\rho_{de}$, where the EoS parameter $w$ depends on time and is
parameterized via the squared adiabatic sound speed $c_{ a}^2$ which is assumed
to be constant. On basis of the general covariant conservation equations for
the interacting dark energy and dark matter and Einstein equations in
Friedmann-Lemaitre-Robertson-Walker metric we analyze the evolution of energy
densities of the hidden components and the dynamics of expansion of the
Universe with two types of interaction: proportional to the sum of densities of
the hidden components and proportional to their product. For the first
interaction the analytical expressions for the densities of dark energy and
dark matter were obtained and analyzed in detail. For the second one the
evolution of densities of hidden components of the Universe was analyzed on
basis of the numerical solutions of their energy-momentum conservation
equations. For certain values of the parameters of these models the energy
densities of dark components become negative. So to ensure that the densities
are always positive we put constraints on the interaction parameter for both
models.
