  Typically, an interactive system evolves towards thermal equilibrium, with
hydrodynamics representing a universal framework for its late-time dynamics.
Classification of the dynamical fixed points (DFPs) of a driven Quantum Field
Theory (with time dependent coupling constants, masses, external background
fields, etc.) is unknown. We use holographic framework to analyze such fixed
points in one example of strongly coupled gauge theory, driven by homogeneous
and isotropic expansion of the background metric - equivalently, a late-time
dynamics of the corresponding QFT in Friedmann-Lemaitre-Robertson-Walker
Universe. We identify DFPs that are perturbatively stable, and those that are
perturbatively unstable, computing the spectrum of the quasinormal modes in the
corresponding holographic dual. We further demonstrate that a stable DFP can be
unstable non-perturbatively, and explain the role of the entanglement entropy
density as a litmus test for a non-perturbative stability. Finally, we
demonstrated that a driven evolution might not have a fixed point at all: the
entanglement entropy density of a system can grow without bounds.
