Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators

Alexandre Mauroy, Rodolphe Sepulchre
2011 IEEE Conference on Decision and Control and European Control Conference  
In this paper, we investigate the behavior of pulsecoupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the approximation of infinite populations. In addition to recovering known stability results of finite populations, we also obtain new stability results for infinite populations. In particular, under a weak coupling assumption, we solve for the continuum model a conjecture still prevailing in the finite dimensional case.
doi:10.1109/cdc.2011.6160621 dblp:conf/cdc/MauroyS11 fatcat:scxx2bkqrzcalpoiewkbfxnbnq