Collective Motion and Optimal Self-Organisation in Self-Driven Systems

We discuss simulations of flocking and the principle of optimal self-organisation during self-driven motion of many similar objects. In addition to driving and interaction the role of fluctuations is taken into account as well. In our models, the particles corresponding to organisms locally interact with their neighbours by choosing at each time step a velocity depending on the directions of motion of them. Our numerical studies of flocking indicate the existence of new types of transitions. As a function of the control parameters both disordered and long-range ordered phases can be observed, and the corresponding phase space domains are separated by singular “critical lines”. In particular, we demonstrate both numerically and analytically that there is a disordered-to-ordered-motion transition at a finite noise level even in one dimension. We also present computational and analytical results indicating that driven systems with repulsive interactions tend to reach an optimal state corresponding to minimal interaction. This extremal principle is expected to be relevant for a class of biological and social systems involving driven interacting entities.