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We perform a dynamical system analysis and a Bayesian model selection for a new set of interacting scenarios in the framework of modified holographic Ricci dark energy models (MHR-IDE). The dynamical analysis shows a modified radiation epoch and a late-time attractor corresponding to dark energy. We use a combination of background data such as type Ia supernovae, cosmic chronometers, cosmic microwave background, and baryon acoustic oscillations measurements. We find evidence against all the MHR-IDE scenarios studied with respect to CDM, when the full joint analysis is considered.

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