Phase space analysis of non-minimally coupled scalar field models in $f(Q)$ gravity

We investigate the cosmological dynamics of a non-minimally coupled scalar field in the framework of symmetric teleparallel $f(Q)$ gravity through a comprehensive phase-space analysis. Considering the coupling $f(Q)=Q+\xi Q\phi^{2}$, we formulate the modified Friedmann equations and recast them into an autonomous system using suitable dimensionless variables. Three representative scalar field potentials, namely a power-law, Kachru-Kallosh-Linde-Trivedi, and a steep exponential potentials are analyzed. For each model, the critical points are determined analytically and their stability is examined through the eigenvalues of the corresponding Jacobian matrix. We find that the non-minimal interaction between the scalar field and the non-metricity scalar naturally gives rise to stable late-time attractor solutions within specific ranges of the coupling parameter $\xi$. In particular, the power-law and KKLT potentials possess stable dark-energy-dominated attractors for $-1/4<\xi<0$, while the steep exponential potential admits multiple accelerating stable solutions with de Sitter-like behavior. The analysis demonstrates that non-minimal $f(Q)$ cosmology can successfully reproduce a late-time acceleration, and provides a robust dynamical framework for studying dark energy scenarios.