Weakly pulse-coupled oscillators: Heterogeneous delays lead to homogeneous phase

This paper studies the effect of heterogeneous delays in networks of weakly pulse-coupled identical oscillators. We develop a new framework to study them by constructing a non-delayed phase model that is equivalent to the original one in the continuum limit. Using existing results for non-delayed phase-coupled oscillators we analyze the delayed system and show how its stability properties depend on the delay distribution. In particular, we show that in some scenarios, heterogeneity, i.e. wider delay distribution, can help reach in-phase synchronization.