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

Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity