Discontinuous codimension-two bifurcation in a Vlasov equation

Abstract

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 analyze one-dimensional spatially periodic Vlasov systems, using 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 detail.