Phase space analysis of $f(Q)$ gravity accelerating cosmological models

The dynamical aspect of accelerating cosmological model has been studied in this paper in the context of modified symmetric teleparallel gravity, the $f(Q)$ gravity. Initially, we have derived the dynamical parameters for two well known form of $f(Q)$ such as: (i) log-square-root form and (ii) exponential form. The equation of state (EoS) parameter for the dark energy in the $f(Q)$ gravity in both the models emerges into a dynamical quantity. At present both the models show the quintessence behavior and behave like the ${\Lambda}$CDM at the late time. Further, the dynamical system analysis has been performed to determine the cosmological behaviour of the models along with its stability behaviour. For both the models the critical points are obtained and analysed the stability at each critical points with phase portraits. The evolutionary behaviour of density parameters for the matter-dominated, radiation-dominated, and dark energy phases are also shown for both the models.