Dynamics and statefinder analysis of a class of sign-changeable
  interacting dark energy scenarios
  We revise the dynamical properties of a class of cosmological models where
the dark sector interacts through an interacting term that changes sign during
evolution. In particular, we obtain the critical points and we investigate the
existence and stability conditions for cosmological solutions, describing
radiation, matter and dark energy dominated eras. We find that all the studied
models admit a stable critical point corresponding to an accelerated phase. We
use background data to find the best fit parameters for one of the studied
models, resulting an interacting parameter with a definite sign within
$1\sigma$ confidence level, consistent with the results of the dynamical system
analysis. We also compute the statefinder parameters and plot the $r-q$ and
$r-s$ planes, where we observe different trajectories when we vary the
interaction parameter for a specific model and when we vary the interacting
scenario. We can in this sense distinguish among models, including
$\Lambda$CDM.
