  We consider directed networks of Winfree oscillators with power law
distributed in- and out-degree distributions. Gaussian and power law
distributed intrinsic frequencies are considered, and these frequencies are
positively correlated with oscillators' in-degrees. The Ott/Antonsen ansatz is
used to derive degree-based mean field equations for the expected dynamics of
networks, and these are numerically analysed. In a variety of cases "explosive"
transitions between either two different steady states or between a steady
state and a periodic solution are found, and these transitions are explained
using bifurcation theory.
