  In a previous paper, we proposed a heterotic dark energy model, called
$\Lambda$HDE, in which dark energy is composed of two components: cosmological
constant (CC) and holographic dark energy (HDE). The aim of this work is to
give a more comprehensive and systematic investigation on the cosmological
implications of the $\Lambda$HDE model. Firstly, we make use of the current
observations to constrain the $\Lambda$HDE model, and compare its cosmology-fit
results with the results of the $\Lambda$CDM and the HDE model. Then, by
combining a qualitative theoretical analysis with a quantitative numerical
study, we discuss the impact of considering curvature on the cosmic evolutions
of fractional HDE density $\Omega_{hde}$ and fractional CC density
$\Omega_{\Lambda}$, as well as on the ultimate cosmic fate. Finally, we explore
the effects of adopting different types of observational data. We find that:
(1) the current observational data cannot distinguish the $\Lambda$HDE model
from the $\Lambda$CDM and the HDE model; this indicates that DE may contain
multiple components. (2) the asymptotic solution of $\Omega_{hde}$ and the
corresponding cosmic fate in a flat universe can be extended to the case of a
non-flat universe; moreover, compared with the case of a flat universe,
considering curvature will make HDE closer to a phantom dark energy. (3)
compared with JLA dataset, SNLS3 data more favor a phantom type HDE; in
contrast, using other types of observational data have no significant impact on
the cosmic evolutions of the $\Lambda$HDE model.
