Cosmological dynamics of interacting dark energy and dark matter in $f(Q)$ gravity

In this work, we explore the behavior of interacting dark energy and dark matter within a model of $f(Q)$ gravity, employing a standard framework of dynamical system analysis. We consider the power-law $f(Q)$ model incorporating with two different forms of interacting dark energy and dark matter: $3\alpha H{\rho }_m$ and $\frac{\alpha }{3H}{\rho }_m{\rho }_{DE}$. The evolution of ${\mathrm{\Omega }}_m,{\mathrm{\Omega }}_r,{\mathrm{\Omega }}_{DE},q$, and $\omega$ for different values of the model parameter $n$ and the interaction parameter $\alpha$ has been examined. Our results show that the universe was dominated by matter in the early stages and will be dominated by dark energy in later stages. Using the observational data, the fixed points are found to be stable and can be represented the de Sitter and quintessence acceleration solutions. We discover that the dynamical profiles of the universe in $f(Q)$ dark energy models are influenced by both the interaction term and the relevant model parameters.