  A one-dimensional rule-based model for flocking, that combines velocity
alignment and long-range centering interactions, is presented and studied. The
induced cohesion in the collective motion of the self-propelled agents leads to
a unique group behaviour that contrasts with previous studies. Our results show
that the largest cluster of particles, in the condensed states, develops a mean
velocity slower than the preferred one in the absence of noise. For strong
noise, the system also develops a non-vanishing mean velocity, alternating its
direction of motion stochastically. This allows us to address the directional
switching phenomenon. The effects of different sources of stochasticity on the
system are also discussed.
