Qualitative behavior of cosmological models combining various matter fields

The late time accelerated expansion of the universe can be realized using scalar fields with given self-interacting potentials. Here we consider a straightforward approach where a three cosmic fluid mixture is assumed. The fluids are standard matter perfect fluid, dark matter, and a scalar field with the role of dark energy. A dynamical system analysis is developed in this context. A central role is played by the equation of state $\omega_{eff}$ which determines the acceleration phase of the models. Determining the domination of a particular fluid at certain stages of the universe history by stability analysis allows, in principle, to establish the succession of the various cosmological eras.