  We consider $N$ oscillators coupled by a mean field as in the Winfree model.
The model is governed by two parameters: the coupling strength $\kappa$ and the
spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled
regime, $\kappa=0$, each oscillator possesses its own natural frequency, and
the difference between the phases of any two oscillators grows linearly in
time. We say that $N$ oscillators are synchronized if the difference between
any two phases is uniformly bounded in time. We identify a new hypothesis for
the existence of synchronization. The domain in $(\gamma,\kappa)$ of
synchronization contains coupling values that are both weak and strong.
Moreover the domain is independent of the number of oscillators and the
distribution of the frequencies. We give a numerical counter-example which
shows that this hypothesis is necessary for the existence of synchronization.
