  We consider a multivariate non-linear Hawkes process in a multi-class setup
where particles are organised within two populations of possibly different
sizes, such that one of the populations acts excitatory on the system while the
other population acts inhibitory on the system. The goal of this note is to
present a class of Hawkes Processes with stable dynamics without assumptions on
the spectral radius of the associated weight function matrix. This illustrates
how inhibition in a Hawkes system significantly affects the stability
properties of the system.
