Varying vacuum models with spatial curvature: a dynamical system perspective

We investigate the qualitative cosmic dynamics of varying vacuum models with the non-flat, homogeneous and isotropic background. In these models, the dark matter interacts with the vacuum energy. We utilize the dynamical system technique to explore the existence and stability of fixed points. The existence of radiation and matter dominated decelerating phase of the universe may be explained in these models. The accelerating universe expansion may also be explained due to the existence of an attractor in these models. Further, the numerical solution technique is incorporated to solve the autonomous systems. These solutions are utilized to illustrate the evolution of cosmographic and statefinder parameters along with the energy conditions. The Milne universe solution exists in the model which is a consequence of spatially curved geometry. The stability criterion of the fixed points reveals that the cosmic history in the considered models may be observationally viable. Furthermore, the strength of interaction terms are constrained using the observational estimates of the cosmographic parameters.