The present work deals with a FLRW cosmological model with spatial curvature and minimally coupled scalar field as the matter content. The curvature term behaves as a perfect fluid with the equation of state parameter \(\omega _{\mathcal {K}}=-\frac{1}{3}\). Using suitable transformation of variables, the evolution equations are reduced to an autonomous system for both power law and exponential form of the scalar potential. The critical points are analyzed with center manifold theory and stability has been discussed. Also, critical points at infinity have been studied using the notion of Poincaré sphere. Finally, the cosmological implications of the critical points and cosmological bouncing scenarios are discussed. It is found that the cosmological bounce takes place near the points at infinity when the non-isolated critical points on the equator of the Poincaré sphere are saddle or saddle-node in nature.

目前的工作涉及以空间曲率和最小耦合标量场作为物质内容的 FLRW 宇宙学模型。曲率项表现为具有状态方程参数 \(\omega _{\mathcal {K}}=-\frac{1}{3}\) 的完美流体。使用适当的变量变换，演化方程被简化为标量势的幂律和指数形式的自治系统。利用中心流形理论分析了临界点并讨论了稳定性。此外，还使用庞加莱球的概念研究了无穷远的临界点。最后，讨论了临界点和宇宙学弹跳场景的宇宙学含义。研究发现，当庞加莱球赤道上的非孤立临界点本质上是鞍点或鞍结点时，宇宙学反弹发生在无穷远点附近。