  In this work, we investigate the dynamics of the interacting dark energy and
dark matter in viable models of $f(R)$ gravity by using a standard framework of
dynamical system analysis. A simple form of the interacting dark energy
$Q=3\alpha H\rho_{m}$ is used to study three viable models of $f(R)$ gravity
which are consistent with local gravity constraints and satisfying conditions
for the cosmological viability. As a result, we find that the fixed points are
slightly modified from those obtained in the standard non-interacting analysis
of $f(R)$ gravity proposed so far in the literature. In our models of adding
this interaction, we find that the dynamical profiles of the universe in the
viable $f(R)$ dark energy models are modified by the interaction term as well
as their relevant model parameters. Moreover, our results yield the correct
cosmological evolution with additional constraint parameter, $\alpha$, from the
interacting dark energy.
