Autonomous systems and attractor behaviors in non-metricity gravity: stability analysis and cosmic acceleration

The cosmological dynamics are rigorously investigated through the systematic application of autonomous system analysis to the gravitational field equations in non-metricity gravity. The systematic procedure to analyze the late-time cosmic acceleration in higher-order non-metricity gravity is demonstrated by exploring non-hyperbolic critical points with the center manifold theory. The stability properties of these critical points are also evaluated based on the analysis of eigenvalues and phase portraits. It is explicitly shown that the stable node can be realized. The critical points of each model are individually analyzed, and their corresponding cosmological implications are derived. The stability properties of these critical points are evaluated based on the analysis of eigenvalues and phase portraits, revealing that each model includes at least one stable node. Furthermore, the evolution plots of the cosmological parameters confirm the models capacity to exhibit accelerated expansion.