  By combining RMF models and equivparticle models with density-dependent quark
masses, we construct explicitly ``a quark Fermi Sea'' and ``a baryonic Fermi
surface'' to model the quarkyonic phase, where baryons with momentums ranging
from zero to Fermi momentums are included. The properties of nuclear matter,
quark matter, and quarkyonic matter are then investigated in a unified manner,
where quarkyonic matter is more stable and energy minimization is still
applicable to obtain the microscopic properties of dense matter. Three
different covariant density functionals TW99, PKDD, and DD-ME2 are adopted in
our work, where TW99 gives satisfactory predictions for the properties of
nuclear matter both in neutron stars and heavy-ion collisions and quarkyonic
transition is unfavorable. Nevertheless, if PKDD with larger slope of symmetry
energy $L$ or DD-ME2 with larger skewness coefficient $J$ are adopted, the
corresponding EOSs are too stiff according to both experimental and
astrophysical constraints. The situation is improved if quarkyonic transition
takes place, where the EOSs become softer and can accommodate various
experimental and astrophysical constraints.
