Synchronization in populations of sparsely connected pulse-coupled oscillators
Department of Epileptology, University of Bonn - Bonn, Germany, Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn - Bonn, Germany and Interdisciplinary Center for Complex Systems, University of Bonn - Bonn, Germany
Received: 22 November 2013
Accepted: 22 January 2014
We propose a population model for δ-pulse–coupled oscillators with sparse connectivity. The model is given as an evolution equation for the phase density which takes the form of a partial differential equation with a non-local term. We discuss the existence and stability of stationary solutions and exemplify our approach for integrate-and-fire–like oscillators. While for strong couplings, the firing rate of stationary solutions diverges and solutions disappear, small couplings allow for partially synchronous states which emerge at a supercritical Andronov-Hopf bifurcation.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 89.75.-k – Complex systems / 84.35.+i – Neural networks
© EPLA, 2014