  In this article we prove the stability of mean field systems as the Winfree
model in the synchronized state. The model is governed by the coupling strength
parameter $\kappa$ and the natural frequency of each oscillator. The stability
is proved independently of the number of os-cillators and the distribution of
the natural frequencies. In order to prove the main result, we introduce the
positive invariant cone and we start by studying the linearized system. The
method can be applied to others mean field models as the Kuramoto model.
