  We consider large-dimensional dynamical systems involving a linear force and
a random force comprising both potential and non-conservative contributions.
Such systems are known to exhibit a topological trivialization phase transition
as the strength of the random force is increased. This is reflected in the
number of stationary points of the dynamical systems that transitions from one
to an exponential in the number of degrees of freedom. We analyze this
transition by means of a replica calculation.
