Synchronization in populations of sparsely connected pulse-coupled oscillators
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.