  So far, there have been no theories or observational data that deny the
presence of interaction between dark energy and dark matter. We extend
naturally the holographic dark energy (HDE) model, proposed by Granda and
Oliveros, in which the dark energy density includes not only the square of the
Hubble scale, but also the time derivative of the Hubble scale to the case with
interaction and the analytic forms for the cosmic parameters are obtained under
the specific boundary conditions. The various behaviors concerning the cosmic
expansion depend on the introduced numerical parameters which are also
constrained. The more general interacting model inherits the features of the
previous ones of HDE, keeping the consistency of the theory.
