  We show that peculiar collective dynamics called slow switching arises in a
population of leaky integrate-and-fire oscillators with delayed, all-to-all
pulse-couplings. By considering the stability of cluster states and symmetry
possessed by our model, we argue that saddle connections between a pair of the
two-cluster states are formed under general conditions. Slow switching appears
as a result of the system's approach to the saddle connections. It is also
argued that such saddle connections easy to arise near the bifurcation point
where the state of perfect synchrony loses stability. We develop an asymptotic
theory to reduce the model into a simpler form, with which an analytical study
of cluster states becomes possible.
