  We investigate a self-interacting dark matter (SIDM) model featuring a
velocity-dependent cross section with an order-of-magnitude resonant
enhancement of the cross section at $\sim 16\,{\rm km}\,{\rm s}^{-1}$. To
understand the implications for the structure of dark matter halos, we perform
N-body simulations of isolated dark matter halos of mass $\sim 10^8\,{\rm
M}_\odot$, a halo mass selected to have a maximum response to the resonance. We
track the core formation and the gravothermal collapse phases of the dark
matter halo in this model and compare the halo evolving with the resonant cross
section with halos evolving with velocity-independent cross sections. We show
that dark matter halo evolution with the resonant cross section exhibits a
deviation from universality that characterizes halo evolution with
velocity-independent cross sections. The halo evolving under the influence of
the resonance reaches a lower minimum central density during core formation. It
subsequently takes about $20\%$ longer to reach its initial central density
during the collapse phase. These results motivate a more detailed exploration
of halo evolution in models with pronounced resonances.
