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.

我们研究了具有非平坦、均匀和各向同性背景的不同真空模型的定性宇宙动力学。在这些模型中，暗物质与真空能量相互作用。我们利用动力系统技术来探索不动点的存在性和稳定性。这些模型可以解释辐射和物质主导的宇宙减速阶段的存在。宇宙加速膨胀也可以用这些模型中吸引子的存在来解释。此外，还结合了数值求解技术来求解自治系统。这些解决方案用于说明宇宙学和探态器参数以及能量条件的演变。模型中存在米尔恩宇宙解，这是空间弯曲几何的结果。不动点的稳定性准则揭示了所考虑模型中的宇宙历史在观测上可能是可行的。此外，相互作用项的强度受到宇宙学参数的观测估计的约束。