  We study the chaotic behavior of the synchronization phase transition in the
Kuramoto model. We discuss the relationship with analogous features found in
the Hamiltonian Mean Field (HMF) model. Our numerical results support the
connection between the two models, which can be considered as limiting cases
(dissipative and conservative, respectively) of a more general dynamical system
of damped-driven coupled pendula. We also show that, in the Kuramoto model, the
shape of the phase transition and the largest Lyapunov exponent behavior are
strongly dependent on the distribution of the natural frequencies.
