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Cosmological dynamics are investigated in detail through systematicprocedures by using the autonomous system analyses of gravitational fieldequations in higher-order symmetric teleparallel equivalent of generalrelativity. The explicit analyses of the late-time cosmic evolutions aredemonstrated for fundamental three types of models under the presence ofnon-relativistic matter (i.e., dark matter and baryons) as well as radiation.The stability of cosmological solutions is also explored by examiningnon-hyperbolic critical points based on the center manifold theory. It is shownthat the acceleration of the universe can be achieved with the higher curvaturegravity. Three different models were considered for the study and dynamicalsystems analysis technique is incorporated. The main finding of the presentanalyses is that cosmological solutions in higher-order symmetric teleparallelequivalent of general relativity can effectively fit observable datasets. Thisis depicted by phase space portraits and qualitative evolution of thecosmological models.

Autonomous system analysis of the late-time cosmological solutions and  their stability in higher-order symmetric teleparallel equivalent of general  relativity