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We investigate a model of interacting dark matter and dark energy given by amodified holographic Ricci cutoff in a spatially flatFriedmann-Robertson-Walker (FRW) space-time. We consider a nonlinearinteraction consisting of a significant rational function of the total energydensity and its first derivative homogeneous of degree one and show that theeffective one-fluid obeys the equation of state of a relaxed Chaplygin gas. Sothat, the universe is dominated by pressureless dark matter at early times andundergoes an accelerated expansion in the far future driven by a strongnegative pressure. We apply the $\chi^{2}$-statistical method to theobservational Hubble data and the Union2 compilation of SNe Ia for constrainingthe cosmological parameters and analyze the feasibility of the modifiedholographic Ricci cutoff. By using the new $Om$ diagnostic method, we find thatthe effective model differs substantially from the $\Lambda$--CDM one, becauseit gets the accelerated expansion faster than the $\Lambda$--CDM model.Finally, a new model with a third component decoupled from the interacting darksector is presented for studying bounds on the dark energy at early times.

Interacting dark matter and modified holographic Ricci dark energy induce a relaxed Chaplygin gas