  We consider a system of random autonomous ODEs introduced by Cugliandolo et
al. [22], which serves as a non-relaxational analog of the gradient flow for
the spherical p-spin model. The asymptotics for the expected number of
equilibria in this model was recently computed by Fyodorov [32] in the
high-dimensional limit, followed a similar computation for the expected number
of stable equilibria by Garcia [38]. We show that for $p > 9$ the number of
equilibria, as well as the number of stable equilibria, concentrate around
their respective averages, generalizing recent results of Subag and Zeitouni
[61, 64] in the relaxational case. In particular, we confirm that this model
undergoes a transition from relative to absolute instability, in the sense of
Ben Arous, Fyodorov, and Khoruzhenko [11].

Probability