In this work, we focus on the phase space singularities of interactive quintessence model in the presence of matter fluid. This model is related to swampland studies, that the outcomes affect all these swampland-related models with the same dynamical system. We shall form the dynamical system corresponding to the cosmological system, which is eventually autonomous, and by using the dominant balances technique we shall investigate the occurrence or not of finite-time singularities. Our results indicate that the dynamical system of the model may develop finite-time singularities, but these are not general singularities, like in the case that the matter fluids were absent, in which case singularities occurred for general initial conditions. Hence, the presence of matter fluids affects the dynamical system of the cosmological system, making the singularities to depend on the initial conditions, instead of occurring for general initial conditions.

中文翻译：

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浅谈沼泽地相关典型暗能量模型中有限时间奇点的出现

在这项工作中，我们专注于在物质流体存在下交互精髓模型的相空间奇点。该模型与沼泽地研究有关，其结果会影响所有这些具有相同动力系统的沼泽地相关模型。我们将形成与宇宙系统相对应的动力系统，它最终是自治的，并且通过使用主导平衡技术我们将研究有限时间奇点的出现与否。我们的结果表明，模型的动力系统可能会产生有限时间的奇点，但这些不是一般的奇点，例如在物质流体不存在的情况下，在一般初始条件下会出现奇点。因此，物质流体的存在会影响宇宙系统的动力系统，