  In a Vlasov equation, the destabilization of a homogeneous stationary state
is typically described by a continuous bifurcation characterized by strong
resonances between the unstable mode and the continuous spectrum. However, when
the reference stationary state has a flat top, it is known that resonances
drastically weaken, and the bifurcation becomes discontinuous. In this article,
we use a combination of analytical tools and precise numerical simulations to
demonstrate that this behavior is related to a codimension-two bifurcation,
which we study in details.
