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.

我们考虑一个具有正曲率空间的均匀和各向同性时空，并研究动态真空能量的宇宙演化。我们利用动力系统技术来研究模型中不动点的存在及其相应的稳定性。相应的宇宙学解描述了晚时加速宇宙具有由辐射和物质主导相位组成的减速时代。自主系统的数值积分揭示了动态真空能量模型的宇宙学解可以描述宇宙的宇宙历史。由于封闭 Friedmann-Robertson-Walker 模型中的动态真空能量，相空间中固定点之间的轨迹也将对应于宇宙的反弹和旋转演化。