Emergence of one- and two-cluster states in populations of globally   pulse-coupled oscillators
  The subject of this paper is a system of phase-oscillators, which are globally pulse-coupled via excitatory interaction. The appearance and stability of one- and two-cluster-states is investigated for a family of unimodal phase-response-curves (PRC). The PRCs and their derivatives are assumed to be zero at the spiking point. We show that there exist stable homoclinic connections of the one-cluster state for PRCs with the maximum located shortly before the spiking point and coexisting stable two-clusters states when the maximum of the PRC is located shortly after the spike. 
Leonhard L\"ucken and Serhiy Yanchuk
nlin.AO