  The well-known Vicsek model describes the dynamics of a flock of
self-propelled particles (SPPs). Surprisingly, there is no direct measure of
the chaotic behavior of such systems. Here, we discuss the dynamical phase
transition present in Vicsek systems in light of the largest Lyapunov exponent
(LLE), which is numerically computed by following the dynamical evolution in
tangent space for up to two million SPPs. As discontinuities in the neighbor
weighting factor hinder the computations, we propose a smooth form of the
Vicsek model. We find a chaotic regime for the collective behavior of the SPPs
based on the LLE. The dependence of LLE with the applied noise, used as a
control parameter, changes sensibly in the vicinity of the well-known
transition points of the Vicsek model.
