  In this paper the cosmological evolution of a holographic dark energy model
with a non-linear interaction between the dark energy and dark matter
components in a FRW type flat universe is analysed. In this context, the
deceleration parameter $q$ and the equation state $w_{\Lambda}$ are obtained.
We found that, as the square of the speed of sound remains positive, the model
is stable under perturbations since early times; it also shows that the
evolution of the matter and dark energy densities are of the same order for a
long period of time, avoiding the so--called coincidence problem. We have also
made the correspondence of the model with the dark energy densities and
pressures for the quintessence and tachyon fields. From this correspondence we
have reconstructed the potential of scalar fields and their dynamics.
