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The modified holographic Ricci dark energy coupled to interactingrelativistic and non-relativistic dark matter is considered in the nonflatFriedmann-Robertson-Walker universe. Through examining the decelerationparameter, one can find that the transition time of the Universe fromdecelerating to accelerating phase in the interacting holographic Ricci darkenergy model is close to that in the $\Lambda$ cold dark matter model. Theevolution of modified holographic Ricci dark energy's state parameter and theevolution of dark matter and dark energy's densities shows that the dark energyholds the dominant position from the near past to the future. By studying thestatefinder diagnostic and the evolution of the total pressure, one can findthat this model could explain the Universe's transition from the radiation toaccelerating expansion stage through the dust stage. According to the $Om$diagnostic, it is easy to find that when the interaction is weak and theproportion of relativistic dark matter in total dark matter is small, thismodel is phantom-like. Through our studying, we find the interaction and therelativistic dark matter's proportion all have great influence on the evolutionof the Universe.

Modified holographic Ricci dark energy coupled to interacting relativistic and non-relativistic dark matter in the nonflat universe