  In this work we study the effects of the non-gravitational exchange energy
(Q) between dark matter (DM) fluid and dark energy (DE) fluid on the background
evolution of the cosmological parameters. A varying equation of state (EOS)
parameter, {\omega}, for DE is proposed. Considering an universe spatially
flat, two distinct coupled models were examined to explore the main
cosmological effects generated by the simultaneous reconstruction of Q and
{\omega} on the shape of the jerk parameter, j, through a slight enhancement or
suppression of their amplitudes with respect to noncoupled scenarios, during
its evolution from the past to the near future. In consequence, j could be used
to distinguish any coupled DE models. Otherwise, the observational data were
used to put stringent constraints on Q and {\omega}, respectively. In such a
way, we used our results as evidences to search possible deviations from the
standard concordance model ({\Lambda}CDM), examining their predictions and
improving our knowledge of the cosmic evolution of the universe.
