  An important characteristic of flocks of birds, school of fish, and many
similar assemblies of self-propelled particles is the emergence of states of
collective order in which the particles move in the same direction. When noise
is added into the system, the onset of such collective order occurs through a
dynamical phase transition controlled by the noise intensity. While originally
thought to be continuous, the phase transition has been claimed to be
discontinuous on the basis of recently reported numerical evidence. We address
this issue by analyzing two representative network models closely related to
systems of self-propelled particles. We present analytical as well as numerical
results showing that the nature of the phase transition depends crucially on
the way in which noise is introduced into the system.
