  We examine the scenario of non-minimally coupled relativistic fluid and
$k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker
universe. By adding a non-minimal coupling term in the Lagrangian level, we
study the variation of Lagrangian with respect to independent variables, which
produces modified scalar field and Friedmann equations. Using dynamical
stability approach in different types of interaction models with two types of
scalar field potential, we explore this coupled framework. Implementing
detailed analysis, we can conclude our models can able to produce stable
late-time cosmic acceleration.
