Cosmological Dynamics of Interacting Dark Energy and Dark Matter in f ( Q ) $f(Q)$ Gravity

In this work, the behavior of interacting dark energy (DE) and dark matter (DM) within a model of $f\left(Q\right)$ gravity is explored, employing the standard framework of dynamical system analysis. The power-law $f\left(Q\right)$ model is considered, incorporating two different forms of interacting DE and DM: $3\alpha H{\rho }_m$ and $\frac{\alpha }{3H}{\rho }_m{\rho }_{\text{DE}}$. The evolution of ${\Omega }_m$, ${\Omega }_r$, ${\Omega }_{\text{DE}}$, $q$, and $\omega$ for different values of the model parameter $n$ and the interaction parameter $\alpha$ is examined. The results indicate that the universe was dominated by matter in the early stages and will be dominated by DE in later stages. The analysis shows that the fixed points are found to be stable and represent the de Sitter and quintessence acceleration solutions. It is found that the dynamical profiles of the universe in $f\left(Q\right)$ DE models are influenced by both the interaction term and the relevant model parameters.