We forecast constraints on cosmological parameters in the interacting dark energy models using the mock data generated for neutral hydrogen intensity mapping (IM) experiments. In this work, we only consider the interacting dark energy models with energy transfer rate $Q=beta Hrho_{rm c}$, and take BINGO, FAST, SKA1-MID, and Tianlai as typical examples of the 21 cm IM experiments. We find that the Tianlai cylinder array will play an important role in constraining the interacting dark energy model. Assuming perfect foreground removal and calibration, and using the Tianlai-alone data, we obtain $sigma(H_0)=0.19$ km s$^{-1}$ Mpc$^{-1}$, $sigma(Omega_{rm m})=0.0033$ and $sigma(sigma_8)=0.0033$ in the I$Lambda$CDM model, which are much better than the results of Planck+optical BAO (i.e. optical galaxy surveys). However, the Tianlai-alone data cannot provide a very tight constraint on the coupling parameter $beta$ compared with Planck+optical BAO, while the Planck+Tianlai data can give a rather tight constraint of $sigma(beta)=0.00023$ due to the parameter degeneracies being well broken by the data combination. In the I$w$CDM model, we obtain $sigma(beta)=0.00079$ and $sigma(w)=0.013$ from Planck+Tianlai. In addition, we also make a detailed comparison among BINGO, FAST, SKA1-MID, and Tianlai in constraining the interacting dark energy models. We show that future 21 cm IM experiments will provide a useful tool for exploring the nature of dark energy and play a significant role in measuring the coupling between dark energy and dark matter.
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