  We compute the homogeneous limit of non-hydrodynamic quasinormal modes
(QNM's) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD)
holographic model for the Quark-Gluon Plasma (QGP) that is able to: i) {\it
quantitatively} describe state-of-the-art lattice results for the QCD equation
of state and higher order baryon susceptibilities with $2+1$ flavors and
physical quark masses up to highest values of the baryon chemical potential
currently reached in lattice simulations; ii) describe the nearly perfect
fluidity of the strongly coupled QGP produced in ultrarelativistic heavy ion
collisions; iii) give a very good description of the bulk viscosity extracted
via some recent Bayesian analyzes of hydrodynamical descriptions of heavy ion
experimental data. This EMD model has been recently used to predict the
location of the QCD critical point in the QCD phase diagram, which was found to
be within the reach of upcoming low energy heavy ion collisions. The lowest
quasinormal modes of the $SO(3)$ rotationally invariant quintuplet, triplet,
and singlet channels evaluated in the present work provide upper bounds for
characteristic equilibration times describing how fast the dense medium returns
to thermal equilibrium after being subjected to small disturbances. We find
that the equilibration times in the different channels come closer to each
other at high temperatures, although being well separated at the critical
point. Moreover, in most cases, these equilibration times decrease with
increasing baryon chemical potential while keeping temperature fixed.
