Globally stable synchronization by inhibitory pulse coupling

We analyze global synchronization of oscillator networks with inhibitory delayed and non-delayed pulse coupling. For a fully-coupled system without delays, we propose simple modifications to the state-of-the-art. We prove that the resulting system converges to full in-phase synchronization of all oscillators from arbitrary initial conditions. For systems with arbitrarily distributed delays we propose a second, related approach. We prove that here a state close to synchrony is globally and asymptotically stable, such that all oscillators lock up to a certain precision from arbitrary initial conditions. The precision of synchronization is determined by the coupling strength and the maximal delay appearing.