  We consider a general swarm model of self-propelling agents interacting
through a pairwise potential in the presence of noise and communication time
delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a
communication time delay in the swarm induces a pattern bifurcation that
depends on the size of the coupling amplitude. We extend these results by
completely unfolding the bifurcation structure of the mean field approximation.
Our analysis reveals a direct correspondence between the different dynamical
behaviors found in different regions of the coupling-time delay plane with the
different classes of simulated coherent swarm patterns. We derive the
spatio-temporal scales of the swarm structures, and also demonstrate how the
complicated interplay of coupling strength, time delay, noise intensity, and
choice of initial conditions can affect the swarm. In particular, our studies
show that for sufficiently large values of the coupling strength and/or the
time delay, there is a noise intensity threshold that forces a transition of
the swarm from a misaligned state into an aligned state. We show that this
alignment transition exhibits hysteresis when the noise intensity is taken to
be time dependent.
