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