2011/01/24 by Leonhard Lücken, Lücken, Leonhard, Serhiy Yanchuk +1
Physics and Astronomy · #34C15 #34D06 #37N25 #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #msc:34C15 #msc:34D06 #msc:37N25 #nlin.AO
paper · pdf · doi:10.48550/arxiv.1101.4487
arxiv created 2011/02/21 · arxiv updated 2015/03/17
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.