Collective motion of organisms in three dimensions

We study a model of flocking in order to describe the transitions during th e collective motion of organisms (e.g., birds) in three dimensions. In this model the particles representing the organisms are self-propelled, i.e., t hey move with the same absolute velocity. In addition, the particles locall y interact by choosing at each time step the average direction of motion of their neighbours and the effects of fluctuations are taken into account as well. We present the first results for large-scale flocking in the presenc e of noise in three dimensions. We show that depending on the control param eters both disordered and long-range ordered phases can be observed. The co rresponding phase diagram has a number of features which are qualitatively different from those typical for the analogous equilibrium models. (C) 1999 Elsevier Science B.V. All rights reserved.