Abstract
We study oscillators with delayed pulse-coupling and complex network topology as simple models for the dynamics of reccurent networks of spiking neurons. We show how the stability of the synchronous state and the speed of synchronization is deterined by the eigenvalues of the coupling matrix. For Gaussian random matrices we use random matrix theory to estimate the bulk eigenvalue spectrum and draw conclusions for synchronization properties of networks. Neural networks, however, typically display sparse connectivity. For a class of sparse random matrices we numerically find similar properties of the eigenvalue spectrum as in the Gaussian ensemble. Steps towards an analytical calculation of the eigenvlaue spectra densities of sparse asymmetric matrices using super-symetry methods are discussed.