We review the observations and the basic laws describing the essential aspects of collective
motion—being one of the most common and spectacular manifestation of coordinated …

Collective behavior in biological systems is a complex topic, to say the least. It runs wildly
across scales in both space and time, involving taxonomically vastly different organisms …

We present a quantitative continuum theory of “flocking”: the collective coherent motion of
large numbers of self-propelled organisms. In agreement with everyday experience, our …

Understanding collective properties of driven particle systems is significant for naturally
occurring aggregates and because the knowledge gained can be used as building blocks …

A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-
propelled particles is introduced. Even though the particles interact strictly locally in a very …

We study a model of flocking in order to describe the transitions during the collective motion
of organisms (eg, birds) in three dimensions. In this model the particles representing the …

We show that the collective properties of self-propelled particles aligning with their
topological (Voronoi) neighbors are qualitatively different from those of usual models where …

We review the past decade's theoretical and experimental studies of flocking: the collective,
coherent motion of large numbers of self-propelled “particles”(usually, but not always, living …

Many animal groups, for example schools of fish or flocks of birds, exhibit complex dynamic
patterns while moving cohesively in the same direction. These flocking patterns have been …

We discuss biologically inspired, inherently non-equilibrium models of self-propelled
particles, in which the particles interact with their neighbors by choosing at each time step …