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.