Role of dynamical vacuum energy in the closed universe: implications for bouncing scenario

We consider a homogeneous and isotropic spacetime having a space of positive curvature and study the cosmic evolution of dynamical vacuum energy. We utilize the dynamical system technique to study the existence of fixed points and their corresponding stability in model. The corresponding cosmological solutions describe late-time accelerating universe having decelerating era composed of radiation and matter-dominated phase. The numerical integration of autonomous system reveals that the cosmological solutions of dynamical vacuum energy model may describe the cosmic history of universe. As a consequence of the dynamical vacuum energy in closed Friedmann-Robertson-Walker model, the trajectories between fixed points in the phase space would also correspond to the bouncing and turnaround universe evolution.