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In this work we present a qualitative description of the evolution of acurved universe when we consider the interacting scheme for the constituents ofthe dark sector. The resulting dynamics can be modeled by a set ofLotka-Volterra type equations. For this model a future singularity is allowed,therefore the cyclic behavior for the energy interchange between the componentsof the universe is present only at some stage of the cosmic evolution. Due tothe presence of the future singularity, the model exhibits global instability.

Qualitative description of the universe in the interacting fluids scheme