  We study an extension of the Winfree model of coupled phase oscillators in
which both natural frequencies and phase-response curves (PRCs) are
heterogeneous. In the first part of the paper we resort to averaging and derive
an approximate model, in which the oscillators are coupled through their phase
differences. Remarkably, this simplified model is the 'Kuramoto model with
distributed shear' (2011 Phys. Rev. Lett. 106 254101). We find that above a
critical level of PRC heterogeneity the incoherent state is always stable. In
the second part of the paper we perform the analysis of the full model for
Lorentzian heterogeneities, resorting to the Ott-Antonsen ansatz. The critical
level of PRC heterogeneity obtained within the averaging approximation has a
different manifestation in the full model depending on the sign of the center
of the distribution of PRCs.
