Qualitative analysis of viscous cosmology

We analyze the effect of higher order viscosity corrections in a spatially homogeneous and isotropic universe. The viscous effects are modeled by introducing a second-order term to the energy density in the equation of state and on the expansion factor. An autonomous dynamical system is then constructed to study the qualitative behavior of the energy density and expansion factor, employing the Raychaudhuri equation and the conservation of energy. We obtain the analytical expressions for the equilibrium points in terms of the model parameters, presenting several phase diagrams. The analysis of these diagrams reveals the presence of bifurcations, which manifest as changes in stability and qualitative behavior. Those changes lead to different configurations for the universe, such as bouncing, rebouncing and cyclic scenarios.