| Summary: | Abstract 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 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 in an interacting parameter with a definite sign within the $$1\sigma $$ 1 σ confidence level, consistent with the results of the dynamical system analysis. We compute the statefinder parameters and plot the $$r-q$$ r - q and $$r-s$$ r - s planes, where we observe different evolutionary trajectories for the interacting scenarios, allowing in this sense to discriminate among dark energy models.
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