Study of late-time universe evolution with an interacting dark sector using two canonical scalar fields

In this paper, we investigated the late-time evolution within the framework of an interactive quintessence model, using qualitative dynamical systems analysis methods complemented by numerical solutions of the evolution equations. According to this model, dark matter and dark energy interact through an interaction term. We demonstrated that the solution provided by this model leads to a scenario of a long enough matter-dominated era continued by a current era of accelerated expansion, where the energy density of the dark matter field rapidly approaches zero, and the evolution is entirely dominated by the dark energy field. Consequently, this model is consistent with the final state of cosmic evolution and can be used as a solution to the cosmic coincidence problem.